Find all solutions in the interval [0, 2π). 2 sin2x = sin x

Solution:

Given 2 sin2x = sin x

These are trigonometric functions

We know that sin2x = 2 sinx cosx

Hence substituting in the given function, we get

2(2 sinx cosx) = sinx

4cosx = 1

cosx = 1/4

x = cos^-1(1/4)

x = 75.5 degrees and 284.48 degrees

Therefore, the solutions in the interval [0, 2π). 2 sin2x = sin x are 75.5 degrees and 284.48 degrees.

Find all solutions in the interval [0, 2π). 2 sin2x = sin x

Summary:

All solutions in the interval [0, 2π). 2 sin2x = sin x are 75.5 degrees and 284.48 degrees.