Precalc Homework Question help!

Question

Find all solutions in [0,2pi) :

 

sin(2t)-sin(t)=0

Answer 1

sin 2t - sin t = 0

2 sin t cos t - sin t = 0        double angle formula

sin t (2 cos t - 1) = 0           factor out sin t

sin t = 0                            zero product rule

{0, π}

2 cos t = 1                         zero product rule

cos t = 1/2

{π/6, 5π/6}