Question

If cosx+ cos 3x - 2 cos 2x =0 then x=?​

Answer 1

Answer:

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Answer 2

Answer:

# Answer-

x=(2n+1)π/4 or x=2nπ where n∈Z

# Solution-

Let's solve this,

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.