A) \[n\pi +{{(-1)}^{n}}\pi /6\]
B) \[n\pi +{{(-1)}^{n}}\pi /2\]
C) \[n\pi +{{(-1)}^{n}}5\pi /6\]
D) \[n\pi +{{(-1)}^{n}}7\pi /6\]
Correct Answer: D
Solution :
| The given equation is |
| \[2{{\sin }^{2}}\theta -3\sin \theta -2=0\] |
| \[\Rightarrow \]\[(2\sin \theta +1)(\sin \theta -2)=0\] |
| \[\Rightarrow \]\[\sin \theta =-\frac{1}{2}\] |
| \[\left[ \because \sin \theta -2=0\operatorname{is}\,not\,possible \right]\] |
| \[\Rightarrow \]\[\sin \theta =\sin (-\pi /6)=\sin (7\pi /6)\] |
| \[\Rightarrow \]\[\theta =n\pi +{{(-1)}^{n}}(-\pi /6)\] |
| \[=n\pi +{{(-1)}^{n}}7\pi /6\] |
| \[\Rightarrow \]Thus, \[\theta =n\pi +{{(-1)}^{n}}7\pi /6\] |
You need to login to perform this action.
You will be redirected in
3 sec
