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

Jul 4, 2018

${\cos}^{n} \left(x + \setminus \frac{\pi}{2}\right) = {\sin}^{n} \left(x\right)$

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.