# Thread: How to solve this?

1. ## How to solve this?

If n ∈ N, solve the equation cos*n x − sin*n x = 1, for x ∈ R.
*n means exponent
∈ means member of

I have no clue how to solve this.

If $x = 0$ , then the solution is $n \in \mathbb{Z}^+$
But the problem here is to determine those positive integers, n, such that the equation is true for all x. More to the point would be to look at $x= \pi/4$ for which cos(x)= sin(x).