I am not sure how to solve this pre-calc question. Show all work please. (general solutions for answer)

Question

tan (3x)cos(2x)=cos(2x)

Answer 1

Case 1: cos(2x) = 0

Any value of x satisfying cos(2x)=0 also satisfies the given equation.

cos(2x) = 0

2x = π/2 + kπ for any integer k

x = π/4 + kπ/2 for any integer k

Case 2: cos(2x) ≠ 0

Then we can divide the given equation by cos(2x).

tan(3x) = 1

3x = π/4 + kπ for any integer k

x = π/12 + kπ/3 for any integer k

So there are the above two sets of solutions.