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

1 Answer
Abhishek K.
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)#

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