A) \[{{i}^{n}}(i\sin \theta +\cos \theta )\]
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) \[\cos \theta +i\sin n\theta \]
Correct Answer: C
Solution :
\[(\sin \theta +i\cos \theta )hn\] \[={{\left[ \cos \left( \frac{\pi }{2}-\theta \right)+i\sin \left( \frac{\pi }{2}-\theta \right) \right]}^{n}}\] \[=\cos n\left( \frac{\pi }{2}-\theta \right)+i\sin n\left( \frac{\pi }{2}-\theta \right)\]
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