Use an Addition or Subtraction Formula to simplify the equat

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

Solution

sin theta cos 3 theta + cos theta sin 3 theta=0

This is of the form

sinA cos B+ cos A sinB=sin(A+B)

So we get

sin(theta + 3theta)=0

sin 4 theta=0

4 theta= sin^-10

theta= pi/4, 2pi/4, 3pi,4,pi,5pi/4, 6pi/4, 7pi/4