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.
Thanks in advance!
Pickslides is saying that for x= 0, cos(x)= cos(0)= 1, sin(x)= sin(0)= 0 and the equation is true for n any positive integer (actually it is true for any integer).
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 $\displaystyle x= \pi/4$ for which cos(x)= sin(x).