Question

Find the general solution of the equation :
cos x + cos 3x - 2 cos 2x = 0

Answer 1

Answer:

cos3x+cosx-2cos2x=0

(cos3x+cosx)-2cos2x=0

Using formula for cosx+cosy

cos3x+cosx = 2cos[(3x+x)/2].cos[(3x-x)/2]

=2cos2x.cosx

Putting this in above eqn

2cos2x.cosx-2cos2x=0

cos2x(cosx-1)=0

Solving for general solutions,

For cos2x=0

x=(2n+1)π/4, n∈Z.

For cosx-1=0

x=2nπ, n∈Z.