tan4x=1 solve the trigonometric equation

Question

Solve the trigonometric equation. Write your answer inn general solution form.

Answer 1

The trigonometric equation tan(4x) = 1

tan(4x) = tan(45)

tan(4x) = tan(π/4)

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

4x = π/4 + nπ

Solution : x = π/16 + nπ /4

For n = 0

x = π/16

For n = 1

x = 5π/16