Finding the value of integral.

Homework Statement

$$\int_0^{\pi} \frac{x(sinx)^{2n}}{(sinx)^{2n}+(cosx)^{2n}}$$ =
A) π2
B) 2π2
C) π2/4
D) π/2

Homework Equations

$$\int_0^π f(x)dx = \int_0^π f(a-x)dx$$

The Attempt at a Solution

If we put n = 1, we get the C option π2/4
But is it true for all n?