( +i , ) ^ n ,is equal to [RPET 2001] - Vidyadip

MCQ

${{(\sin \theta +i\,\cos \theta )}^{n}}\,$is equal to [RPET 2001]

A
$\cos n\theta +i\,\sin n\theta $
B
$\sin n\theta +i\,\cos n\theta $
✓
$\cos n\left( \frac{\pi }{2}-\theta \right)+i\,\sin n\left( \frac{\pi }{2}-\theta \right)$
D
None of these

✓

Answer

Correct option: C.

$\cos n\left( \frac{\pi }{2}-\theta \right)+i\,\sin n\left( \frac{\pi }{2}-\theta \right)$

C

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