Question

Find all solutions to the equation sin(3x)cosx-sinx cos(3x)=0 on the interval [0,2pi]

Answer 1

Please have in mind that sin(A - B) = sin(A)cos(B) - cos(A)sin(B) 
So what we do is:
sin(3x)cos(x) - sin(x)cos(3x) = 0 => sin(3x - x) = 0 

sin(2x) = 0 

2x = 0, π, 2π, 3π, 4π 

x = 0, π/2, π, 3π/2, 2π
With this, even though not giving you all the answers, will help you greatly to get them. I know you will get the answers with no problems.