sec -1 (1/ 2x2 – 1) = 2 cos -1 x
Take x = cos θ
Where θ = cos -1 x
Here LHS = sec -1 (1/ 2x2 – 1)
Substituting the value of x
= sec -1 (1/ 2cos2 θ– 1)
It can be written as
= sec -1 (1/ cos2 θ)
We get
= sec -1 (sec2 θ)
= 2 θ
By substituting the value of θ
= 2 cos -1 x
= RHS
Hence, it is proved.