If 2Cosθ = x+1/x So, Prove That ? Cos2θ = 1/2(x²+1/x²)

2 Answers
May 20, 2018

LHS=cos2θ

=2cos2θ1

=2(12(x+1x))21

=12(x2+1x2+2x1x)1

=12(x2+1x2)+1221

=12(x2+1x2)=RHS

May 20, 2018

Sqaring the given equation we get
cos(θ)=14(x2+1x2+2) then by multiplying by 2 we get
2cos2(θ)=12(x2+1x2)+1 from here we get
2cos2(θ)1=12(x2+1x2)

Explanation:

we used (x+1x)2=x2+1x2+2
cos(2x)=2cos2(x)1