Find all solutions to the equation. sin2x + sin x = 0

Solution:

Given equation is

sin2x + sin x = 0

We know the trigonometric identity: sin2x = 2sinxcosx

2sinxcosx + sinx =0

Take sinx as common from the terms

sinx(2cosx + 1) =0

If the product is zero, then either of the terms is zero

sinx = 0 or 2cosx + 1 = 0

sinx = 0 or cosx = -1/2

x= sin^-1(0) or x= cos^-1(-1/2)

x= nπ or x= -nπ/4.

Find all solutions to the equation. sin2x + sin x = 0

Summary:

The solutions for the equation sin2x + sin x = 0 are x = nπ or x = -nπ/4.