If 2tan^-1x=sin^-1K. What will be the value of k?

1 Answer
May 3, 2018

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

Explanation:

Let tan^(-1)x=a then

rarrtana=x

rarrsin2a=(2tana)/(1+tan^2a)=(2x)/(1+x^2)

rarr2a=sin^(-1)((2x)/(1+x^2))

rarr2tan^(-1)x=sin^(-1)((2x)/(1+x^2))

Given that 2tan^(-1)x=sin^(-1)k By comparing, we get,

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