Assertion (A): \[\frac{\sin \theta -2{{\sin }^{3}}\theta }{2{{\cos }^{3}}\theta -\cos \theta }=\tan \theta ,\] where \[\theta \] is acute angle. |
Reason (R): For acute angle A, \[\tan A=\frac{\sin A}{\cos A}\]and \[{{\sin }^{2}}A+{{\cos }^{2}}A=1.\] |
A) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A)
B) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A)
C) Assertion (A) is true but Reason (R) is false
D) Assertion (A) is false but Reason (R) is true
Correct Answer: A
Solution :
[a] We have. |
\[\operatorname{L}.H.S=\frac{\sin \theta -2{{\sin }^{3}}\theta }{2{{\cos }^{3}}\theta -\cos \theta }=\frac{\sin \theta (1-2si{{n}^{2}}\theta )}{\cos \theta (2{{\cos }^{2}}\theta -1)}\] |
\[\tan \theta =\frac{[1-2(1-co{{s}^{2}}\theta )]}{(2{{\cos }^{2}}\theta -1)}\] \[[\ \ {{\sin }^{2}}\theta =1-{{\cos }^{2}}\theta ]\] |
\[\tan \theta \cdot \frac{(2co{{s}^{2}}\theta -1)}{(2{{\cos }^{2}}\theta -1)}=\tan \theta =\operatorname{R}.H.S\] |
\[\therefore \] Assertion: True: Reason: True and it is the correct explanation of Assertion. |
You need to login to perform this action.
You will be redirected in
3 sec