2 x - 3x - 5x = - Vidyadip

MCQ

$2\cos x - \cos 3x - \cos 5x = $

✓
$16{\cos ^3}x{\sin ^2}x$
B
$16{\sin ^3}x{\cos ^2}x$
C
$4{\cos ^3}x{\sin ^2}x$
D
$4{\sin ^3}x{\cos ^2}x$

✓

Answer

Correct option: A.

$16{\cos ^3}x{\sin ^2}x$

a
(a) $2\,\cos x - \cos \,3x - \cos \,5x = 2\cos x(1 - \cos 4x)$

$ = 2\cos x\,2{\sin ^2}2x$$ = 4\,\cos x\,{\sin ^2}\,2x $

$= 16\,{\sin ^2}x\,{\cos ^3}x$.

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