Question

If sin^-1 2a/1+a² + sin^-1 2b/1+b² = 2 tan^-1x then show that x = a+b/1-ab.

Answer 1

sin^-1 2a/1+a² + sin^-1 2b/1+b² = 2 tan^-1x

Answer 2

sin^-1 2a/1+a² + sin^-1 2b/1+b² = 2 tan^-1x

=>2tan^-1 a + 2tan^-1 b = 2 tan^-1x

=>tan^-1 a + tan^-1 b = tan^-1x

=>tan^-1[ (a +  b )/(1-ab)]= tan^-1x

=> x= (a+b)/(1-ab)