Question

Let $f(x)=\sin ^{-1}\left(\frac{2 x}{1+x^2}\right)$ and $g(x)=\cos ^{-1}\left(\frac{x^2-1}{x^2+1}\right)$, then the value of $(f(10)-g(100))$ is equal to

• A. $\pi-2\left(\tan ^{-1}(10)+\tan ^{-1}(100)\right)$
• B. 0
• C. $2\left(\tan ^{-1}(100)-\tan ^{-1}(10)\right)$
• D. $2\left(\tan ^{-1}(10)-\tan ^{-1}(100)\right)$

Answer 1

Answer: (C)

Correct answer is (c) $2\left(\tan ^{-1}(100)-\tan ^{-1}(10)\right)$