Question

Solve:  sin(2 tan ^-1 x)=1

Answer 1

sin( 2tan^-1x) = 1
∴ `2((tan(tan^-1x)))/ (1 + tan^2(tan^-1x))= 1 {sin 2θ = (2tanθ}/(1+ tan^2theta)}`

`(2x)/(1+x^2)=1`

 x² + 1 = 2x
x² + 1 - 2x = 0
(x-1)² = 0 
x - 1 = 0
x = 1