Question

Find all solutions in the interval [0, 2π). cos x = sin x.

Answer 1

cos x = sin x
cos x - sin x = 0
cos^2 x - 2cos x sin x + sin^2 x = 0
1 - 2sin x cos x = 0
1 - sin 2x = 0
sin 2x = 1
2x = arc sin 1
x = (arc sin 1)/2
x = 45, 135