A) \[\cos n\theta +i\,\sin n\theta \]
B) \[\sin n\theta +i\,\cos n\theta \]
C) \[\cos n\left( \frac{\pi }{2}-\theta \right)+i\,\sin n\left( \frac{\pi }{2}-\theta \right)\]
D) None of these
Correct Answer: C
Solution :
\[{{(\sin \theta +i\cos \theta )}^{n}}\]\[={{\left[ \cos \left( \frac{\pi }{2}-\theta \right)+i\sin \left( \frac{\pi }{2}-\theta \right) \right]}^{n}}\] = \[\cos n\left( \frac{\pi }{2}-\theta \right)+i\sin n\left( \frac{\pi }{2}-\theta \right)\].
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