Question

If x > 1, then write the value of sin−1 `((2x)/(1+x^2))` in terms of tan⁻¹ x.

Answer 1

sin⁻¹ `((2x)/(1+x^2))`

= π - 2 tan^-1 x      `[because2tan^-1x=pi-sin^-1((2x)/(1+x^2))  "for"  x>1]`