Trig question i dont understand

Question

Give all radian solutions to cos7xcos2x+sin7xsin2x=1/2. How do I do this?

Answer 1

cosAcosB + sinAsinB = cos(A-B)

 

So, cos(7x)cos(2x) + sin(7x)sin(2x) = cos(7x-2x) = cos(5x) = 1/2

 

5x = π/3 + 2kπ or 5π/3 + 2kπ

 

x = π/15 + 2kπ/5 or π/3 + 2kπ/5, where k = 0, ±1, ±2,...