Use trigonometric identities to solve each equation in the interval [0, 2π). sin x = cos x

Question

Use trigonometric identities to solve each equation in the interval [0, 2π).

sin x = cos x

If there are some answers that will not work, please say why.

Answer 1

sinx = cosx

x =45 +180n where n= any integer

x = ...-135, 45, 225, 405, ... degrees

an infinite number of solutions

= pi/4 +pin radians where n = any integer

Answer 2

Answer 3

sin(x)=cos(x)

Divide by cos(x)

sin(x)/cos(x) = 1

sin(x)/cos(x)= tan(x) =1

tan^-1(1) = x

x = π/4 or 5π/4 in [0,2π)