Solve for the exact solutions in the interval [ 0,2π ) .

Question

 cos(2x)cos(x)−sin(2x)sin(x)=−√(3)/2

Answer 1

cos(A+B) = cosAcosB - sinAsinB

So, we have cos(3x) = -√3/2

3x = 5π/6 + 2kπ or 7π/6 + 2kπ, k = 0, 1, -1, 2, -2, ...

x = 5π/18 + 2kπ/3 or 7π/18 + 2kπ/3

Plug in k = 0, 1, 2 to get the 6 solutions that lie in the given interval.