Question

ICOS
cos (3π/4 + x) – cos (3π/4 - x) = – √2 sin x​

Answer 1

Step-by-step explanation:

$\cos( \frac{3\pi}{4} + x ) - \cos( \frac{3\pi}{4} - x) \\ = \cos( 135+ x ) - \cos(135 - x) \\ = \cos(135) \cos(x) - \sin(135) \sin(x) - ( \cos(135) \cos(x) + \sin(135) \sin(x) ) \\ = \cos(135) \cos(x) - \sin(135) \sin(x) - \cos(135) \cos(x) - \sin(135) \sin(x) \\ = - 2 \sin(135) \sin(x) \\ = - 2 \times \frac{ \sqrt{2} }{2} \sin(x) \\ = - \sqrt{2} \sin(x)$

PROVED

Identity used:

cos(a+b) = cos(a).cos(b) - sin(a).sin(b)

cos(a-b) = cos(a).cos(b) + sin(a).sin(b)

HOPE IT HELPS :D