7cos(2x) = 7sin(4x)

Question

How do I solve the following equation?

7sin(4x) = 7cos(2x)

I know of the trig identity where sin(2x) = 2sin(x)cos(x), but I'm not sure how this would apply for this particular problem where it's doubled.

I am applying it to an Area Between Curves question, where I am asked to solve for the area enclosed by the curves:

y = 7sin(4x), y = 7cos(2x), x = 0, x = pi/4

Thank you!

Answer 1

7sin(4x) = 7cos(2x)

=> 7 (2sin2xcos2x) = 7cos2x

=>2sin2x = 1

=> sin2x = 1/2

=> 2x = nπ + (-1)^n π/6

or x = nπ/2 + (-1)^n π/12  where n ∈ Z