Let f(x)= sin -1((2 x/1+x2)) and g(x)= cos -1((x2-1/x2+1)), then the value of (f(10)-g(100)) is equal to

Question

Let f(x)= sin -1((2 x/1+x2)) and g(x)= cos -1((x2-1/x2+1)), then the value of (f(10)-g(100)) is equal to (A) π-2( tan -1(10)+ tan -1(100)) (B) 0 (C) 2( tan -1(100)- tan -1(10)) (D) 2( tan -1(10)- tan -1(100))

Tardigrade Admin · Accepted Answer

Correct answer is (c) 2( tan -1(100)- tan -1(10))

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

$π - 2 (tan^{- 1} (10) + tan^{- 1} (100))$

0

$2 (tan^{- 1} (100) - tan^{- 1} (10))$

$2 (tan^{- 1} (10) - tan^{- 1} (100))$

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

Q. Let f(x)=sin−1(1+x22x​) and g(x)=cos−1(x2+1x2−1​), then the value of (f(10)−g(100)) is equal to

π−2(tan−1(10)+tan−1(100))

0

2(tan−1(100)−tan−1(10))

2(tan−1(10)−tan−1(100))

Correct answer is (c) 2(tan−1(100)−tan−1(10))

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

$π - 2 (tan^{- 1} (10) + tan^{- 1} (100))$

$2 (tan^{- 1} (100) - tan^{- 1} (10))$

$2 (tan^{- 1} (10) - tan^{- 1} (100))$

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