Question

If sin⁻1((2a)/(1+a²)) -cos⁻1((1-b²)/(1+b²)) =tan⁻1((2x)/(1-x²)), then what is the value of x?

• A. \(\dfrac{a}{b}\)
• B. \(ab\)
• C. \(\dfrac{b}{a}\)
• D. (a-b)/(1+ab)

Hint:

Memorize inverse–trigonometric identities for faster simplification.

Answer 1

The Correct Option is D

Using standard identities: sin⁻1((2a)/(1+a²))=2tan⁻1a cos⁻1((1-b²)/(1+b²))=2tan⁻1b Thus, tan⁻1x=tan⁻1((a-b)/(1+ab))