Question

100 Points! Algebra question. Photo attached. Solve the equation. Please show as much work as possible. Thank you!

Answer 1

`\sin(x) + \sin(2x) = 0`

`\sin(x) + 2 \sin(x) \cos(x) = 0`

`( \sin(x) )(1 + 2 \cos(x) ) = 0`

sin(x) = 0 or 1 + 2cos(x) = 0

2cos(x) = -1

cos(x) = -1/2

x = kπ or x = 2π/3 + 2kπ or

x = 4π/3 + 2kπ

(k is an integer)