How to solve and get the general solution without a calculator

Question

How to solve and then get the general solution of 2 cos2xcos 3pi/10 - 2 sin2xsin 3pi/10 = √2

Answer 1

2cos(2x + 3π/10) = √2; cos(2x + 3π/10) = √2/2;

2x + 3π/10 = π/4 + 2πn; 2x = π/4 - 3π/10 + 2πn; x = - π/40 + πn or

2x + 3π/10 = 7π/4 + 2πn, 2x = 7π/4 - 3π/10 + 2πn, x = 29π/40 + πn, n = 0, ±1, ±2, ...

Answer 2

sin u cos v - cos u sin v = sin (u - v)