use an addition or subtraction formula to simplify the equation

Question

For cos x cos 3x - sin x sin 3x=0 use an addition or subtraction formula to simplify the equation and then find all solutions of the equation in the interval [0, pi)

 

the answer is 

x1=

x2=

x3=

x4=

with x1<x2<x3<x4

 

 

Answer 1

 

cos x cos 3x - sin x sin 3x

= cos(x+3x)

= cos(4x)

Solve cos(4x) = 0 in [0, pi],

4x = k*pi+pi/2.

Picking k = 0, 1, 2, 3, you have x = pi/8, 3pi/8, 5pi/8, 7pi/8.