Question

Is xcos2x even or odd?

Answer 1

Odd.

Explanation:

Let, `f(x)=xcos2x`.

Then, `f(-x)=(-x)cos(2(-x))`,

`=-xcos(-2x)`,

`=-xcos2x..................................[because, cos(-theta)=costheta]`.

`rArr f(-x)=-f(x)`.

Consequently, `f` is odd.