Question

cos x +cos 2x =0 use exact values in radians

Answer 1

start by replacing \(\cos(2x)\) by \(2\cos^2(x)-1\) and solve the quadratic equation

Answer 2

cos2x =2cos^2 x -1
cos x +cos 2x =0
cosx+2cos^2 x -1=0
let u=cosx
2u^2 +u-1=0
(u+1)(2u-1)=0
u=-1 or u=1/2
cosx=-1 or cosx=1/2
x=pi,3pi,.... or x=pi/3 or -pi/3 ....