Question

If tan^-1(√(1 + x²) - √(1 - x²))/(√(1 + x²) + √(1 - x²)) = β, then x =

(A) tanβ

(B) ±√((1 - tanβ)/(1 + tanβ))

(C) ±√sin2β

(D) ±√cos2β 

Answer 1

Correct option (C) ±√sin2β   

Explanation:

Squaring both sides, we get

Using componendo and dividendo, we get

x² = sin2β

⇒  x = ± √sin2β