Find all solutions in the interval [0, 2π). cos x = sin x

Solution:

Given equation cos x = sin x

All possible values which satisfy the given trigonometric equation are called solutions of the given trigonometric equation.

The trigonometric equations involve trigonometric functions of angles as variables.

Divide by cos x on both sides

We get 1= sin x/ cos x

1 = tan x

x = tan^-1(1)

In the given interval [0, 2π), we have solutions as π/4, 3π/4 and 7π/4

Find all solutions in the interval [0, 2π). cos x = sin x

Summary:

All solutions in the interval [0, 2π) when cos x = sin x are π/4, 3π/4 and 7π/4.