Question

The value of `cos(pi/4 + x) - cos(pi/4 - x)` is ______.

विकल्प

• `sqrt(2) sin x`

• `- sqrt(2) sin x`

• `sqrt(2) cos x`

• `- sqrt(2) cos x`

Answer 1

The value of `cos(pi/4 + x) - cos(pi/4 - x)` is `- sqrt(2) sin x`.

Explanation:

`cos(pi/4 + x) - cos(pi/4 - x)` 

= `cos  pi/4 cos x - sin  pi/4 sin x - cos  pi/4 cos x - sin  pi/4 sin x`

= `- 2 sin  pi/4 sin x`

= `- 2/sqrt(2) sin x`

= `- sqrt(2) sin x`