( + i , )^n ,is equal to - Vidyadip

MCQ

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

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
(c)${(\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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