Use an Addition or Subtraction Formula to simplify the equat

Use an Addition or Subtraction Formula to simplify the equation. cos(theta) cos(2 theta) + sin(theta) sin(2 theta) = Squareroot 3/2 Find all solutions in the interval [0, 2 pi). (Enter your answers as a comma-separated list.) theta =

Solution

cos theta cos 2 theta + sin theta sin 2theta= sqrt3/2

cos (A-B)= cos A cos B+ sin A sin B

On using that formula we get

cos(theta - 2theta)= sqrt3/2

cos(-theta)= sqrt3/2

cos theta= sqrt3/2

theta= pi/6

In th interval [0,2pi)

theta=pi/6,11pi/6