Prove the following: 2tan^(-1)x=cos^(-...

Prove the following:
`2tan^(-1)x=cos^(-1)((1-x^(2))/(1+x^(2))),xge0`

Verified by Experts

The correct Answer is:

`x^(x cos x)[cos x. (1+ log x)-x sin xlog x]-(4x)/((x^(2)-1)^2)`.

Similar Questions

Explore conceptually related problems

Prove the following: 2tan^(-1)x=sin^(-1)((2x)/(1+x^(2))),+x+le1

Prove the following: 2tan^(-1)x=tan^(-1)((2x)/(1-x^(2))),-1ltxlt1

Write the value of x for which 2tan^(-1)x = cos^(-1)[(1-x^(2))/(1+x^(2))] holds:

Write the set of the value of x for which 2tan^(-1)x="cos"^(-1)(1-x^(2))/(1+x^(2)) holds.

y = cos^(-1)((1-x^2)/(1+x^2)), 0 lt x lt 1 .

Prove the following: sin^(-1)(2xsqrt(1-x^(2)))=2cos^(-1)x,-1/(sqrt(2))lexle1/(sqrt(2))

Prove the following: sin^(-1)(2xsqrt(1-x^(2)))=2sin^(-1)x,-1/(sqrt(2))lexle1/(sqrt(2))

Prove That : tan^(-1)sqrt(x)=1/2"cos"^(-1)(1-x)/(1+x),x epsilon[0,1]

The value of sin [tan ^(-1)((1-x^(2))/(2 x))+cos ^(-1)((1-x^(2))/(1+x^(2)))]=