Use an Addition or Subtraction Formula to simplify the equation

Question

Use an Addition or Subtraction Formula to simplify the equation.

cos(θ) cos(2θ) + sin(θ) sin(2θ) = 3/2

Find all solutions in the interval [0, 2π). (Enter your answers as a comma-separated list.)

Answer 1

cos(2T-T) = cos2T cos T + sin 2T sin T = sqrt(3)/2

cos(T) = sqrt(3)/2

T = 30, so the solution is flavors of 30 degrees

30,150,210,330

check:

cos(30) cos(60) + sin(30)sin(60) =

sqrt(3)/2 * 1/2 + (1/2)(sqrt(3)/2) =

sqrt(3)/4 + sqrt(3)/4 =

sqrt(3)/2

yes