Solve the equation :cosx+cos3x−2cos2x=0
cosx+(4cos3x−3cosx)−2(2cos2x−1)=0
cosx+4cos3x−3cosx−4cos2x+2=0
4cos3x−4cos2x−2cosx+2=0
4cos2x(cosx−1)−2(cosx−1)=0
(4cos2x−2)(cosx−1)=0
(2cos2x−1)(cosx−1)=0
∴cos2x=1/2
or cos2x=cos2(π/3)
∴x=xπ±π/3
and if cosx−1=0
cosx=1
cosx=cos0
∴x=2xπ