( +i , ) ^ 4 ( +i , ) ^ 5 = [RPET 2002] - Vidyadip

MCQ

$\frac{{{(\cos \alpha +i\,\sin \alpha )}^{4}}}{{{(\sin \beta +i\,\cos \beta )}^{5}}}=$ [RPET 2002]

A
$\cos (4\alpha +5\beta )+i\,\sin (4\alpha +5\beta )$
B
$\cos (4\alpha +5\beta )-i\,\sin (4\alpha +5\beta )$
✓
$\sin (4\alpha +5\beta )-i\cos (4\alpha +5\beta )$
D
None of these

✓

Answer

Correct option: C.

$\sin (4\alpha +5\beta )-i\cos (4\alpha +5\beta )$

C

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