Choose the correct answer If tan^-1{(√(1 + x^2) -√(1 - x^2))/(√(1 + x^2) + √(1 - x^2))} = α, then x^2 =

Question

Choose the correct answer

If tan^-1\(\{\frac{\sqrt{1+x^2}-\sqrt{1-x^2}}{\sqrt{1+x^2}+\sqrt{1-x^2}}\}\) = α, then x² = 

A. sin 2α

B. sin α

C. cos 2α

D. cos α

Answer 1

Correct option is A. sin 2α

We are given that,

Now, we need to simplify it in order to find x². So, rationalize the denominator by multiplying and dividing by

\(\sqrt{1+x^2}-\sqrt{1-x^2}.\)

Note the denominator is in the form: (x + y)(x – y), where

(x + y)(x – y) = x² – y²

So,

Numerator: Applying the algebraic identity in the numerator, (x – y)² = x² + y² – 2xy.

We can write as,

Substituting values of Numerator and Denominator from (ii) and (iii) in equation (i),