A) \[2\theta =\frac{\pi }{2}-\alpha \]
B) \[\theta =2n\pi \pm \left( \frac{\pi }{2}-\alpha \right)\]
C) \[\theta =\frac{n\pi +{{(-1)}^{n}}\alpha }{2}\]
D) \[\theta =n\pi \pm \left( \frac{\pi }{4}-\frac{\alpha }{2} \right)\]
Correct Answer: D
Solution :
\[\cos 2\theta =\cos \left( \frac{\pi }{2}-\alpha \right)\Rightarrow 2\theta =2n\pi \pm \left( \frac{\pi }{2}-\alpha \right)\] \[\Rightarrow \] \[\theta =n\pi \pm \left( \frac{\pi }{4}-\frac{\alpha }{2} \right)\].
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