A) \[\frac{\sin ({{2}^{n}}\theta )}{{{2}^{n}}\sin \theta }\]
B) \[\frac{cos({{2}^{n}}\theta )}{{{2}^{n}}\cos \theta }\]
C) \[\frac{cosn\theta }{{{2}^{n}}\cos \theta }\]
D) \[\frac{sin({{2}^{n}}\theta )}{\sin \theta }\]
Correct Answer: A
Solution :
[a] By setting n=1, given expression becomes \[\cos \theta \]. By setting n=1, option (1) becomes \[\frac{\sin 2\theta }{2\sin \theta }=\frac{2\sin \theta \cos \theta }{2\sin \theta }=\cos \theta \].
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