Question

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

Answer 1

Use the double angle identity sin2x=2sinxcosx.

sin2x+sinx=0
2sinxcosx+sinx=0
sinx(2cosx+1)=0
sinx=0 implies that x is a multiple of 2npi where n is an integer.
cosx=-1/2 implies that x is multiples of 7pi/6 and 11pi/6.

Answer 2

for sinx, x can also be multiples of pi.

Answer 3

What am I supposed to do about the "find all solutions."?

Answer 4

State the general solutions for x.

Answer 5

Which would be?

Answer 6

follow what @seitys is saying.

Answer 7

Okay.