1 + 2x + 4x + 6x = - Vidyadip

MCQ

$1 + \cos 2x + \cos 4x + \cos 6x = $

A
$2\cos x\cos 2x\cos 3x$
B
$4\sin x\,\cos 2x\cos 3x$
✓
$4\cos x\cos 2x\cos 3x$
D
None of these

✓

Answer

Correct option: C.

$4\cos x\cos 2x\cos 3x$

c
(c) $1 + \cos \,\,2x + \cos \,4x + \cos \,6x$

$ = (1 + \cos \,6x) + (\cos \,2x + \cos \,4x)$

$ = 2\,{\cos ^2}3x + 2\,\cos \,3x\,\cos x $

$= 2\,\cos \,3x\,(\cos \,3x + \cos \,x)$

$ = 4\,\cos x\,\cos \,2x\,\cos \,3x$.

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