Who is asking: Teacher
sin 2x = cos 3x
Primary question: how do you handle the cos 3x?
You can use the multiple angle expressions for sin(x+y) and cos(x+y) to write cos(3x) in terms of cos(x) and sin(x).
= cos(2x)cos(x) - sin(2x)sin(x)
= [1 - 2sin2(x)]cos(x) - 2sin(x)cos(x)sin(x)
= cos(x) - 2sin2(x)cos(x) - 2sin2(x)cos(x)
= cos(x) - 4sin2(x)cos(x)
Equating the expressions for cos(3x) and sin(2x) you can extract a factor of cos(x) and be left with a quadratic in sin(x) that can be solved using the general quadratic.Paul and Chris