I need to find all exact solutions on the interval [0, 2pi) for the equation below

Question

sin(7x)cos(6x)-sin(6x)cos(7x)=1/2

Answer 1

Sin (A - B) = SinA CosB - CosA SinB is the identity to solve this problem.

Then Sin7x Cos6x - Cos7x Sin 6x

Sin(7x-6x) = Sin(x) = 1/2

x = 30° or Π/6

Answer 2

Us.e the difference formula for sine