What are the solutions for this trig equation?

Question

interval:(0, 2pi) 

cosx/3-sinx/3=0 

Answer 1

The trigonometric equation cos(x/3) - sin(x/3) = 0

cos(x/3) = sin(x/3)

1 = sin(x/3)/cos(x/3)

tan(x/3) = 1

Let x/3 = t

tan(t) = tan(π/4)

The general solution of tan(θ) = tan(α) is θ = nπ + α, where n is an integer.

θ = t, α = π/4

For n = 0, t = (0)π + π/4 = π/4

x/3 = t ⇒x = 3t = 3π/4

For n = 1, t = (1)π + π/4 = 5π/4

x/3 = t ⇒x =3t = 15π/4

The solutions are in the interval (0, 2pi) is 3π/4.