Question

Find the general solution of the equation cosx+cos3x-2.cos 2x=0.​

Answer 1

Answer:

x = 2xπ

Step-by-step explanation:

=cosx+(4cos 3x−3cosx)−2(2cos2x−1)=0

=cosx+4cos 3 x−3cosx−4cos 2x+2=0

=4cos 3 x−4cos 2 x−2cosx+2=0

=4cos 2x(cosx−1)−2(cosx−1)=0

=(4cos 2 x−2)(cosx−1)=0

=(2cos 2x−1)(cosx−1)=0

∴cos 2

x=1/2

or cos 2

x=cos 2(π/3)

∴x=xπ±π/3

and if cosx−1=0

cosx=1

cosx=cos0

∴x=2xπ