Solve Equation: cos(2x) = sin(2x)

Question

Solution lies in (0, 2pi] 

Answer 1

The trigonometric equation is cos(2x) = sin(2x).

Divide each side by cos (2x).

sin(2x)/cos(2x) = cos(2x)/cos(2x)

sin(2x)/cos(2x) = 1

tan (2x) = 1

tan (2x) = tan(π/4)

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

⇒ 2x = nπ + π/4

x = π/2(n + 1/4).

If n = 0, then x = π/2(0 + 1/4) = π/8,

If n = 1, then x = π/2(1 + 1/4) = 5π/8,

If n = 2, then x = π/2(2 + 1/4) = 9π/8, and

If n = 3, then x = π/2(3 + 1/4) = 13π/8,.............

The solutions are x = π/8, x = 5π/8, x = 9π/8, and x = 13π/8 in the interval (0, 2π].