Question

Cos (x+π/2)=sinx...but if this whole function is powered by even number what will be the answer?

Answer 1

If you're asking if

`cos^n(x+\pi/2) = sin^n(x)`

for every even `n`, the answer is yes. Actually, its' true for every exponent `n`.

Since you have the initial equality `x=y`, then `x^n=y^n` must always hold.