-
question_answer1)
The value of \[\mathbf{sin}\,\mathbf{45}{}^\circ .\,\mathbf{cos}\,\mathbf{30}{}^\circ -\mathbf{cos}\,\mathbf{45}{}^\circ .\,\mathbf{sin}\,\mathbf{30}{}^\circ \] is equal to _________
A)
\[\frac{\sqrt{3}+1}{2}\] done
clear
B)
\[\frac{\sqrt{6}-\sqrt{2}}{4}\] done
clear
C)
\[\frac{\sqrt{2}}{4}(\sqrt{3}+\sqrt{2})\] done
clear
D)
\[\frac{\sqrt{6}-\sqrt{2}}{2\sqrt{2}}\] done
clear
E)
None of these done
clear
View Solution play_arrow
-
question_answer2)
The value of \[\mathbf{tan}\,\mathbf{10}{}^\circ .\mathbf{tan}\text{ }\mathbf{20}{}^\circ .\mathbf{tan}\,\mathbf{30}{}^\circ .\mathbf{tan}\,\mathbf{45}{}^\circ .\]\[\mathbf{tan}\,\mathbf{60}{}^\circ .\mathbf{tan}\,\mathbf{70}{}^\circ .\mathbf{tan}\,\mathbf{80}{}^\circ \]is:
A)
0 done
clear
B)
\[-\]1 done
clear
C)
1 done
clear
D)
2 done
clear
E)
None of these done
clear
View Solution play_arrow
-
question_answer3)
If \[\mathbf{sin }\theta \mathbf{ =}\frac{\mathbf{p}}{\mathbf{q}}\] then \[\mathbf{cos}\theta \]equals to _________
A)
\[\mathbf{ }\sqrt{{{q}^{2}}-{{p}^{2}}}\mathbf{ }\] done
clear
B)
\[\frac{\sqrt{{{q}^{2}}-{{p}^{2}}}}{q}\] done
clear
C)
\[\sqrt{{{p}^{2}}-{{q}^{2}}}\] done
clear
D)
\[\frac{\sqrt{{{p}^{2}}+{{q}^{2}}}}{q}\] done
clear
E)
None of these done
clear
View Solution play_arrow
-
question_answer4)
The value of cos\[\theta \] in terms of tan\[\theta \] is
A)
\[\frac{1}{\sqrt{1-{{\tan }^{2}}\theta }}\] done
clear
B)
\[\frac{1}{\sqrt{1+{{\tan }^{2}}\theta }}\] done
clear
C)
\[\frac{\sqrt{1-{{\tan }^{2}}\theta }}{\sqrt{1+{{\tan }^{2}}\theta }}\] done
clear
D)
\[\frac{1}{\sqrt{3-3{{\tan }^{2}}\theta }}\] done
clear
E)
None of these done
clear
View Solution play_arrow
-
question_answer5)
\[Si{{n}^{\mathbf{4}}}\theta \text{ }+\text{ }Co{{s}^{\mathbf{4}}}\theta \]equals to__________
A)
\[1+2\text{ }si{{n}^{2}}\theta \text{ }co{{s}^{2}}\theta \text{ }\] done
clear
B)
\[2\text{ }si{{n}^{2}}\theta \text{ }co{{s}^{2}}\theta \text{ }-\text{ }1\] done
clear
C)
\[1-2\text{ si}{{\text{n}}^{\text{2}}}\theta \text{ co}{{\text{s}}^{\text{2}}}\theta \] done
clear
D)
\[3+2si{{n}^{2}}\theta \text{ }co{{s}^{2}}\theta \] done
clear
E)
None of these done
clear
View Solution play_arrow
-
question_answer6)
Simplify \[\frac{\mathbf{si}{{\mathbf{n}}^{\mathbf{2}}}\mathbf{30{}^\circ }\mathbf{.co}{{\mathbf{s}}^{\mathbf{2}}}\mathbf{ 30{}^\circ - ta}{{\mathbf{n}}^{\mathbf{2}}}\mathbf{30{}^\circ }\mathbf{.ta}{{\mathbf{n}}^{\mathbf{2}}}\mathbf{60{}^\circ }}{{{\mathbf{(sin 60{}^\circ + cos60{}^\circ )}}^{\mathbf{2}}}}\]
A)
\[\frac{-1}{2\sqrt{3}-4}\] done
clear
B)
\[\frac{-13(\sqrt{3}+2)}{4}\] done
clear
C)
\[\frac{1}{4+2\sqrt{3}}\] done
clear
D)
\[\frac{13}{8}(\sqrt{3}-2)\] done
clear
E)
None of these done
clear
View Solution play_arrow
-
question_answer7)
If 4 tan A = 3, then the value of \[\frac{\mathbf{3co}{{\mathbf{s}}^{\mathbf{3}}}\mathbf{ A - 5 si}{{\mathbf{n}}^{\mathbf{3}}}\mathbf{ A}}{\mathbf{2cos A+5}}\] is _______ (where A is an acute angle)
A)
\[\frac{18}{275}\] done
clear
B)
\[\frac{19}{175}\] done
clear
C)
\[\frac{20}{105}\] done
clear
D)
\[\frac{19}{275}\] done
clear
E)
None of these done
clear
View Solution play_arrow
-
question_answer8)
Which among the following is different? |
\[\mathbf{2}\,\mathbf{co}{{\mathbf{s}}^{\mathbf{2}}}\mathbf{30{}^\circ }-\mathbf{ 1,}\]\[\mathbf{1 }-\mathbf{ 2 si}{{\mathbf{n}}^{\mathbf{2}}}\mathbf{30{}^\circ }\] |
\[\mathbf{co}{{\mathbf{s}}^{\mathbf{2}}}\mathbf{30{}^\circ }-\mathbf{ si}{{\mathbf{n}}^{\mathbf{2}}}\mathbf{30{}^\circ , }\frac{\mathbf{1}-\mathbf{ta}{{\mathbf{n}}^{\mathbf{2}}}\mathbf{ 30{}^\circ }}{\mathbf{1+ta}{{\mathbf{n}}^{\mathbf{2}}}\mathbf{30{}^\circ }}\] |
A)
\[2\text{ }co{{s}^{2}}30{}^\circ -1~\] done
clear
B)
\[1\text{ }-\text{ }2 si{{n}^{2}}30{}^\circ \] done
clear
C)
\[co{{s}^{2}}30{}^\circ -si{{n}^{2}}30{}^\circ \] done
clear
D)
\[\frac{1-{{\tan }^{2}}\text{ 30}{}^\circ }{1+{{\tan }^{2}}\text{ 30}{}^\circ }\] done
clear
E)
None of these done
clear
View Solution play_arrow
-
question_answer9)
Which among the following is not similar? |
\[\mathbf{sin 60{}^\circ , 2 sin 30{}^\circ }\mathbf{.cos 30{}^\circ }\]\[\frac{\mathbf{2tan 30{}^\circ }}{\mathbf{1+ta}{{\mathbf{n}}^{\mathbf{2}}}\mathbf{30{}^\circ }}\mathbf{,}\frac{\sqrt{\mathbf{3}}}{\mathbf{2}}\] |
A)
\[sin\text{ }60{}^\circ ~\] done
clear
B)
\[2\text{ }sin\text{ }30{}^\circ .cos\text{ }30{}^\circ ~\] done
clear
C)
\[\frac{2tan 30{}^\circ }{1+ta{{n}^{2}}30{}^\circ }\] done
clear
D)
\[\frac{\sqrt{3}}{2}\] done
clear
E)
None of these done
clear
View Solution play_arrow
-
question_answer10)
If \[\mathbf{sin}\theta -\mathbf{cos}\theta =\mathbf{0}\], then find the value of \[\mathbf{(si}{{\mathbf{n}}^{\mathbf{4}}}\theta \mathbf{+co}{{\mathbf{s}}^{\mathbf{4}}}\theta \mathbf{)}\], where \[\theta \] is a, acute angle.
A)
\[\frac{1}{3}\] done
clear
B)
\[\frac{\sqrt{2}}{4}\] done
clear
C)
\[\frac{1}{2}\] done
clear
D)
\[\frac{\sqrt{2}}{2}\] done
clear
E)
None of these done
clear
View Solution play_arrow
-
question_answer11)
If \[\mathbf{tan }\theta \mathbf{=}{{\sqrt{\mathbf{3}}}^{{}}}\]then find the value of\[\mathbf{si}{{\mathbf{n}}^{\mathbf{2}}}\theta \mathbf{-co}{{\mathbf{s}}^{\mathbf{2}}}\theta \], where \[\theta \] is acute angle.
A)
\[\frac{1}{2}\] done
clear
B)
\[\frac{-1}{3}\] done
clear
C)
\[\frac{-1}{2}\] done
clear
D)
\[\frac{1}{4}\] done
clear
E)
None of these done
clear
View Solution play_arrow
-
question_answer12)
Simplified form of \[\left( \mathbf{1 + co}{{\mathbf{t}}^{\mathbf{2}}}\theta \right)\mathbf{ }\left( \mathbf{1 - cos }\theta \right)\mathbf{ }\left( \mathbf{1 + cos }\theta \right)\]is ______
A)
1 done
clear
B)
0 done
clear
C)
\[Cosec\text{ }\theta ~~~~~\] done
clear
D)
\[Sin\text{ }\theta ~~~~~~~~\] done
clear
E)
None of these done
clear
View Solution play_arrow
-
question_answer13)
If\[\mathbf{m=sin}\theta \mathbf{+cos}\theta \] and \[\mathbf{n = sin }\theta \mathbf{ -cos }\theta \], then which of the following is true?
A)
\[{{m}^{2}}+{{n}^{2}}=2\] done
clear
B)
\[{{m}^{2}}+{{n}^{2}}=1\] done
clear
C)
\[{{m}^{2}}-{{n}^{2}}=1\] done
clear
D)
\[{{m}^{2}}+{{n}^{2}}=3\] done
clear
E)
None of these done
clear
View Solution play_arrow
-
question_answer14)
The value of \[\mathbf{cot 5{}^\circ }\mathbf{.cot 15{}^\circ }\mathbf{.cot}\text{ }\mathbf{25{}^\circ }\mathbf{.cot 35{}^\circ }\mathbf{.cot45}{}^\circ \]\[\mathbf{.cot 55{}^\circ }\mathbf{.cot}\mathbf{.65{}^\circ }\mathbf{.cot 75{}^\circ }\mathbf{.cot 85{}^\circ }\]is _____.
A)
\[\sqrt{3}\] done
clear
B)
\[\frac{1}{\sqrt{3}}\] done
clear
C)
1 done
clear
D)
\[2\sqrt{3}\] done
clear
E)
None of these done
clear
View Solution play_arrow
-
question_answer15)
\[\frac{\mathbf{Sin 75{}^\circ }\mathbf{.cos 25{}^\circ }\mathbf{.tan 50{}^\circ }}{\mathbf{Sin 65{}^\circ }\mathbf{.cos15{}^\circ }\mathbf{.cot40{}^\circ }}\]
A)
1 done
clear
B)
\[\mathbf{~}\frac{1}{2}\] done
clear
C)
\[\mathbf{~}\frac{1}{3}\] done
clear
D)
\[\mathbf{~}\frac{1}{4}\] done
clear
E)
None of these done
clear
View Solution play_arrow
-
question_answer16)
If \[\mathbf{2 sin }\alpha \mathbf{=}\sqrt{\mathbf{3}}\] then \[\frac{\mathbf{ta}{{\mathbf{n}}^{\mathbf{2}}}\alpha \mathbf{+3}\mathbf{.cot}\alpha }{\mathbf{co}{{\mathbf{t}}^{\mathbf{2}}}\alpha \mathbf{+2tan}\alpha }\] is equal to ______ (where \[\alpha \] is an acute angle)
A)
\[\frac{3(\sqrt{3}+1)}{1+6\sqrt{3}}\] done
clear
B)
\[\frac{-\,45-51\sqrt{3}}{-107}\] done
clear
C)
\[\frac{50\sqrt{3}+45}{-106}\] done
clear
D)
\[\frac{-\,51\sqrt{3}}{107}\] done
clear
E)
None of these done
clear
View Solution play_arrow
-
question_answer17)
In a \[\Delta \text{ }\mathbf{PQR}\], right-angled at Q, and if PR \[-\] QR 2 cm and PQ = 10 cm then _______
A)
\[cosec\text{ }R\text{ }=\frac{13}{12}\] done
clear
B)
\[sec\text{ }R\text{ }=\frac{13}{5}\] done
clear
C)
\[\tan \text{ }P\text{ }=\frac{12}{5}\] done
clear
D)
All the above done
clear
E)
None of these done
clear
View Solution play_arrow
-
question_answer18)
If \[\left( {{p}^{2}}-{{q}^{2}} \right)~~\] \[\mathbf{sin}\theta +\text{ }\mathbf{2pq}\text{ }\mathbf{cos}\text{ }\theta =\text{ }{{\mathbf{p}}^{\mathbf{2}}}-\text{ }{{\mathbf{q}}^{\mathbf{2}}}\], then the value of tan\[\theta \] is ________
A)
\[\frac{p+q}{2pq}\] done
clear
B)
\[\frac{p-q}{2pq}\] done
clear
C)
\[\frac{{{p}^{2}}-{{q}^{2}}}{2pq}\] done
clear
D)
\[\frac{{{p}^{2}}+{{q}^{2}}}{2pq}\] done
clear
E)
None of these done
clear
View Solution play_arrow
-
question_answer19)
If \[\theta \] is an acute angle and 4\[\mathbf{cos}\theta \mathbf{+4}\sqrt{\mathbf{3}}\] \[\mathbf{sin}\theta =\mathbf{8}\text{ }\mathbf{sin}\theta \text{ }\mathbf{cos}\theta +2-\sqrt{3}\], then which one among the following is correct?
A)
\[sin \theta =\frac{\sqrt{3}}{2}\] done
clear
B)
\[\cos \theta =\frac{1}{2}\] done
clear
C)
\[\theta =30{}^\circ \] done
clear
D)
\[\tan \theta =\sqrt{3}\] done
clear
E)
None of these done
clear
View Solution play_arrow
-
question_answer20)
For \[\mathbf{0{}^\circ }<\theta <\mathbf{90{}^\circ },\] if \[\sqrt{\mathbf{2}}\mathbf{(sin}\theta \mathbf{+cos}\theta \mathbf{)}\]\[=\mathbf{1+2 sin}\theta \mathbf{ cos}\theta \] then which among the following is not correct?
A)
\[Sin\text{ }\theta -cos\text{ }\theta =0\] done
clear
B)
\[Sin\text{ }\theta +cos\text{ }\theta =0\] done
clear
C)
\[\theta =45{}^\circ \] done
clear
D)
\[Sin\text{ }2\theta =2\text{ }cos\left( \theta +15 \right)\] done
clear
E)
None of these done
clear
View Solution play_arrow
-
question_answer21)
Simplify: \[\frac{\mathbf{3 sin 67{}^\circ }}{\mathbf{5 cos 23{}^\circ }}\mathbf{+}\frac{\mathbf{5}}{\mathbf{2}}\frac{\mathbf{Sec39{}^\circ }\mathbf{.cos51{}^\circ }}{\mathbf{(1+co}{{\mathbf{t}}^{\mathbf{2}}}\mathbf{ 51)}}\mathbf{+}\frac{\mathbf{8}}{\mathbf{9}}\]\[\mathbf{(cose}{{\mathbf{c}}^{\mathbf{2}}}\mathbf{42{}^\circ }-\mathbf{ta}{{\mathbf{n}}^{\mathbf{2}}}\mathbf{48{}^\circ )}\]
A)
\[3\frac{89}{90}\] done
clear
B)
\[2\frac{81}{90}\] done
clear
C)
\[cos\text{ }67{}^\text{o}+\,sec\text{ }39{}^\text{o}\] done
clear
D)
\[\frac{3}{5}\cos 67{}^\circ +\frac{5}{2}\sec 51{}^\circ +\frac{8}{9}{{\cot }^{2}}\text{48}{}^\circ \] done
clear
E)
None of these done
clear
View Solution play_arrow
-
question_answer22)
In a \[\Delta \,\mathbf{PQR}\], \[\angle Q\] is a right angle and QT is a perpendicular drawn on PR. If PR = 15 cm and QT = 5 cm, then the value of \[\frac{\mathbf{tan}\,\mathbf{P+tan}\,\mathbf{R}}{\mathbf{tan}\,\mathbf{R}\,\mathbf{.}\,\mathbf{tan}\,\mathbf{P}}\] is _________
A)
\[\frac{1}{3}\] done
clear
B)
2 done
clear
C)
\[\frac{1}{2}\] done
clear
D)
3 done
clear
E)
None of these done
clear
View Solution play_arrow
-
question_answer23)
Find the value of\[\frac{{{\mathbf{k}}^{\mathbf{2}}}\mathbf{-1}}{{{\mathbf{k}}^{\mathbf{2}}}\mathbf{+1}}\]if\[\mathbf{k}=\mathbf{sec}\theta -\mathbf{tan}\theta \].
A)
\[Sin\text{ }\theta \] done
clear
B)
\[Cos\text{ }\theta \] done
clear
C)
\[-Sin\text{ }\theta \] done
clear
D)
\[-Cos\text{ }\theta \] done
clear
E)
None of these done
clear
View Solution play_arrow
-
question_answer24)
Which among the following statements is/ are true?
A)
The value of \[sin\text{ }\theta \]decreases as \[\theta \] increases. \[(when\text{ }0{}^\circ <\theta <90{}^\circ )\] done
clear
B)
The value of \[cos\text{ }\theta \] increases \[(when\text{ }0{}^\circ <\theta <90{}^\circ )\] done
clear
C)
\[Sin\text{ }\left( A\text{ }+\text{ }B \right)\text{ }=\text{ }sin~A.\cos B\] done
clear
D)
The value of tan \[\theta \]is always greater than \[sin\text{ }\theta .\] done
clear
E)
None of these done
clear
View Solution play_arrow
-
question_answer25)
If \[\mathbf{cosec }\theta \mathbf{-cot }\theta \mathbf{=3}\] then find the positive value of\[\mathbf{cos}\text{ }\theta \].
A)
\[\,\frac{4}{5}\] done
clear
B)
1 done
clear
C)
0 done
clear
D)
2 done
clear
E)
None of these done
clear
View Solution play_arrow
-
question_answer26)
If \[\mathbf{A=}\frac{\mathbf{1}}{\mathbf{1+sin }\theta }\mathbf{+}\frac{\mathbf{1}}{\mathbf{1-sin }\theta }\], then A equals to _________ .
A)
\[{{\sec }^{2}}\theta \] done
clear
B)
\[2{{\sec }^{2}}\theta \] done
clear
C)
\[{{\cos }^{2}}\theta \] done
clear
D)
\[2{{\cos }^{2}}\theta \] done
clear
E)
None of these done
clear
View Solution play_arrow
-
question_answer27)
The value of \[log\,\,\cos 0{}^\circ +\log \,\,\cos 1{}^\circ +\] \[\log \,\,\cos 2{}^\circ +\_\_\_\_\_\_+log\,cos90{}^\circ \] is equal to _________
A)
1 done
clear
B)
\[-\]1 done
clear
C)
0 done
clear
D)
Undefined done
clear
E)
None of these done
clear
View Solution play_arrow
-
question_answer28)
If \[\mathbf{sin}\theta \text{ }+\text{ }\mathbf{cos}\text{ }\theta =\text{ }\mathbf{p}\], then the value of \[\mathbf{si}{{\mathbf{n}}^{\mathbf{6}}}\theta \mathbf{+co}{{\mathbf{s}}^{\mathbf{6}}}\theta \] equals to _________
A)
\[\frac{4+3({{p}^{2}}-1)}{4}\] done
clear
B)
\[\frac{4-3{{({{p}^{2}}-1)}^{2}}}{4}\] done
clear
C)
\[4-3\left( {{p}^{2}}-1 \right)~~~~~~~~~~~~~~~~~\] done
clear
D)
\[4-3{{\left( {{p}^{2}}-1 \right)}^{2}}\] done
clear
E)
None of these done
clear
View Solution play_arrow
-
question_answer29)
If \[\mathbf{co}{{\mathbf{s}}^{\mathbf{2}}}\theta \text{ }+\text{ }\mathbf{cos}\text{ }\theta =\mathbf{1}\], then find the value of \[\mathbf{si}{{\mathbf{n}}^{\mathbf{4}}}\theta \text{ }+\text{ }\mathbf{si}{{\mathbf{n}}^{\mathbf{2}}}\theta \].
A)
0 done
clear
B)
1 done
clear
C)
\[-\]1 done
clear
D)
\[\cos \theta \] done
clear
E)
None of these done
clear
View Solution play_arrow
-
question_answer30)
The value of \[\mathbf{lo}{{\mathbf{g}}_{\mathbf{sec}\theta }}\mathbf{co}{{\mathbf{s}}^{\mathbf{3}}}\theta \] \[\left[ \left( \mathbf{cos}\theta -\mathbf{sin}\theta {{)}^{\mathbf{2}}}\mathbf{+2sin}\theta \text{ }\mathbf{cos}\text{ }\theta \right) \right]\] is _______
A)
0 done
clear
B)
\[-\]1 done
clear
C)
2 done
clear
D)
\[-\]3 done
clear
E)
None of these done
clear
View Solution play_arrow
-
question_answer31)
If \[\mathbf{sin}\alpha +\text{ }\mathbf{sin}\beta +\mathbf{sin}\gamma =\mathbf{3}\] then the value of \[\mathbf{si}{{\mathbf{n}}^{\mathbf{3}}}\alpha \mathbf{+si}{{\mathbf{n}}^{\mathbf{3}}}\beta \mathbf{+si}{{\mathbf{n}}^{\mathbf{3}}}\gamma -\mathbf{2sin}\alpha \mathbf{.sin}\beta \] \[-\,\mathbf{2sin}\beta \mathbf{sin}\gamma \mathbf{-2sin}\gamma \mathbf{.sin}\alpha \] is ________
A)
\[-\]1 done
clear
B)
\[-\]2 done
clear
C)
\[-\]3 done
clear
D)
0 done
clear
E)
None of these done
clear
View Solution play_arrow
-
question_answer32)
If \[\mathbf{co}{{\mathbf{t}}^{\mathbf{4}}}\theta \text{ }\mathbf{-}\text{ }\mathbf{co}{{\mathbf{t}}^{\mathbf{2}}}\theta \mathbf{=1}\], then the value of \[\mathbf{co}{{\mathbf{s}}^{\mathbf{4}}}\theta \text{ }+\text{ }\mathbf{co}{{\mathbf{s}}^{\mathbf{2}}}\theta \] is _________
A)
\[-\]1 done
clear
B)
1 done
clear
C)
0 done
clear
D)
2 done
clear
E)
None of these done
clear
View Solution play_arrow
-
question_answer33)
\[\mathbf{cosec}\theta \left( \mathbf{sec}\theta -\mathbf{1} \right)-\mathbf{cot}\theta \text{ }\left( \mathbf{1}-\mathbf{cos}\,\theta \right)\]equals to _______
A)
\[tan\text{ }\theta \text{ }+\text{ }sin\text{ }\theta \] done
clear
B)
\[tan\text{ }\theta \text{ }+\text{ }\cot \text{ }\theta \] done
clear
C)
\[tan\text{ }\theta \text{ }+\text{ }\cos \text{ }\theta \] done
clear
D)
\[tan\text{ }\theta \text{ }-\sin \text{ }\theta \] done
clear
E)
None of these done
clear
View Solution play_arrow
-
question_answer34)
\[\frac{{{\mathbf{(sin}\theta \mathbf{+cos}\theta \mathbf{)}}^{\mathbf{2}}}-\mathbf{3sin}\theta \mathbf{cos}\theta }{\mathbf{cos}\theta \mathbf{(sec}\theta -\mathbf{cosec}\theta \mathbf{)}}\], \[\frac{\mathbf{si}{{\mathbf{n}}^{\mathbf{2}}}\theta -\mathbf{co}{{\mathbf{s}}^{\mathbf{2}}}\theta }{\mathbf{si}{{\mathbf{n}}^{\mathbf{3}}}\theta \mathbf{+co}{{\mathbf{s}}^{\mathbf{3}}}\theta }\] is equal to________
A)
\[cos\text{ }\theta\] done
clear
B)
sin \[\theta\] done
clear
C)
\[\tan \theta \] done
clear
D)
\[\cos \theta\] done
clear
E)
None of these done
clear
View Solution play_arrow
-
question_answer35)
\[\frac{\mathbf{Si}{{\mathbf{n}}^{\mathbf{3}}}\theta \mathbf{+co}{{\mathbf{s}}^{\mathbf{3}}}\theta }{\mathbf{Sin}\theta \mathbf{(1-sin}\theta \mathbf{ cos}\theta \mathbf{)}}+\frac{\mathbf{si}{{\mathbf{n}}^{\mathbf{3}}}\theta \mathbf{-co}{{\mathbf{s}}^{\mathbf{3}}}\theta }{\mathbf{sin}\theta \mathbf{(1+sin}\theta \mathbf{cos}\theta \mathbf{)}}\]equals to ________
A)
2 sin\[\theta \] done
clear
B)
2\[cos\,\theta \] done
clear
C)
1 done
clear
D)
2 done
clear
E)
None of these done
clear
View Solution play_arrow
-
question_answer36)
If \[\mathbf{cot}\theta \,(\mathbf{1+sin}\theta )=\mathbf{2}\text{ }\mathbf{m}\] and \[\mathbf{cot}\theta ~\]\[(\mathbf{1}-\mathbf{sin}\theta )=\mathbf{2n}\] then \[{{\left( {{\mathbf{m}}^{\mathbf{2}}}-{{\mathbf{n}}^{\mathbf{2}}} \right)}^{\mathbf{2}}}\]equals to _________.
A)
2 mm done
clear
B)
mn done
clear
C)
4 mn done
clear
D)
3mn done
clear
E)
None of these done
clear
View Solution play_arrow
-
question_answer37)
If\[\mathbf{cos}\,\mathbf{3}x\mathbf{=4}\,\mathbf{co}{{\mathbf{s}}^{\mathbf{3}}}\mathbf{30{}^\circ }-\mathbf{3co}{{\mathbf{s}}^{\mathbf{3}}}\mathbf{0{}^\circ }\]then the value of x is ________
A)
0 done
clear
B)
\[30{}^\circ \] done
clear
C)
\[20{}^\circ \] done
clear
D)
\[15{}^\circ \] done
clear
E)
None of these done
clear
View Solution play_arrow
-
question_answer38)
If \[\mathbf{sin 2x=}\frac{\mathbf{2tan 30{}^\circ }}{\mathbf{1+ ta}{{\mathbf{n}}^{\mathbf{2}}}\mathbf{ 30}}\] , then the value of \[\frac{\mathbf{1}-\mathbf{ta}{{\mathbf{n}}^{\mathbf{2}}}\mathbf{x}}{\mathbf{1+ta}{{\mathbf{n}}^{\mathbf{2}}}\mathbf{x}}\]is equal to____ (where\[0{}^\circ <x<90{}^\circ \])
A)
Sin x done
clear
B)
Cos 3x done
clear
C)
0 done
clear
D)
1 done
clear
E)
None of these done
clear
View Solution play_arrow
-
question_answer39)
If \[\frac{\mathbf{sin}\theta \mathbf{+cos}\theta }{\mathbf{sin}\theta -\mathbf{cos}\theta }\mathbf{=3}\] then the value of \[\mathbf{si}{{\mathbf{n}}^{\mathbf{4}}}\theta -\mathbf{co}{{\mathbf{s}}^{\mathbf{4}}}\theta \]
A)
\[\frac{4}{3}\] done
clear
B)
\[\frac{3}{4}\] done
clear
C)
\[\frac{5}{3}\] done
clear
D)
\[\frac{3}{5}\] done
clear
E)
None of these done
clear
View Solution play_arrow
-
question_answer40)
If \[\mathbf{cos}\alpha =\mathbf{sin14}\,\alpha \] (where \[\mathbf{0}{}^\circ \mathbf{< 14}\alpha \mathbf{< 90{}^\circ }\]), then find the value of \[\mathbf{sin5}\alpha \mathbf{+cos}\left( \mathbf{12}\alpha -\mathbf{ 27{}^\circ } \right)\]\[-\,\mathbf{cosec}\left( \mathbf{3}\alpha \mathbf{+ 12{}^\circ } \right).\]
A)
\[\sqrt{2}\] done
clear
B)
\[\sqrt{2}-1\] done
clear
C)
\[\frac{\sqrt{2}-1}{2}\] done
clear
D)
\[\sqrt{2}+1\] done
clear
E)
None of these done
clear
View Solution play_arrow