|sinx|=|cosx|?

Case 1 : When 0 ≤ x ≤ π/2 or π ≤ x ≤ 3π/2 :
sinx and cosx have the same sign, i.e.
sinx = cosx
sinx/cosx = 1
tanx = 1
x = π/4 x = π + (π/4)
x = π/4, 5π/4

Case 2 : When π/2 < x < π or 3π/2 < x ≤ 2π :
sinx and cosx have different signs, i.e.
sinx = -cosx
sinx/cosx = -1
tanx = -1
x = π - (π/4), 2π - (π/4)
x = 3π/4, 7π/4

Refer to both Case 1 and Case 2.
For 0 ≤ x ≤ 2π
x = π/4, 3π/4, 5π/4, 7π/4

General solution :
x = nπ ± (π/4)
where n = 0, 1, 2, 3 ......