Simplest form of `(1+ tan^2 A)/(1+cot^2A)` IS

Simplest form of (1+ tan^2 A) /(1+cot^2 A) IS

Simplest form of (1 - cos^2A) (1 + cot^2A) is .....................

The simplest form of tan^(-1)((x)/(a+sqrt(a^(2)-x^(2)))) is :

The simplest form of cot^-1 (1/(sqrt(x^2-1))) , |x|>1 is

Let f(x) = cos(tan^(-1) ( sin ( cot^(-1)x))) . The simplest form of f(x) can be written as ((x^(2) +A)/(x^(2) +B))^(1//2) . Then the value of (A + B) is ………………

Let f(x) = cos(tan^(-1) ( sin ( cot^(-1)x))) . The simplest form of f(x) can be written as ((x^(2) +A)/(x^(2) +B))^(1//2) . Then the value of (A + B) is ………………

Let f(x) = cos(tan^(-1) ( sin ( cot^(-1)x))) . The simplest form of f(x) can be written as ((x^(2) +A)/(x^(2) +B))^(1//2) . Then the value of (A + B) is ………………

Write the simplest form : tan^(-1)(1/sqrt(x^2 -1)) , |x|gt1

Write the simplest form : tan^(-1)(1/sqrt(x^2 -1)) , |x|gt1