Question

find all solutions to the problem
cosx=sinx

Answer 1

One way of getting at least a rough idea of the solution(s) here would be to graph both the sine and the cosine functions on the same set of axes. Determine by inspection the x-values at which the two graphs intersect (meaning that sin x = cos x).

Answer 2

A completely different approach would be this: divide both sides of the given equation by cos x. This produces the new but equivalent equation tan x = 1. Solve this new equation for x.