Math Need Help Please FAST

Question

Solve: sin(2x)cosx=0 for [0,2π)

Answer 1

sin2x =0 use the double angle formula to get

2sinxcosx =0 set each factor = 0

sinx =0, cosx =0

sinx = 0 when x =0 or pi,

cosx = 0 when x =pi/2 or 3pi/2

x= 0, pi/2, pi or 3pi/2 (don't include 2pi because it's not in the interval [0,2pi) due to the closed parenthesis. Had it ended with a bracket [0,2pi] then 2pi would have been another soution)

Answer 2

This can happen when sin(2x) = 0 or cos(x) = 0

sin(2x) = 0 when x = 0, π/2

cos(x) = 0 when x = π/2, 3π/2

x = 0, π/2, 3π/2