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

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

Prove: (1-tan^2A)/(cot^2A-1)=tan^2A

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( (cos x)/(1+sin x))

Prove the following identities : ((1 + tan^(2) A) cot A)/(cosec^(2) A) = tan A

prove (1 + tan^2A) / (1 + cot^2A) = [(1 - tan A) / (1 - cotA)] ^2 = tan^2A

Write the following function in the simplest form: tan^(-1)x/(sqrt(a^2-x^2)) , |x|lta

Write the following functions in the simplest form: (i) tan^(-1){x/(sqrt(a^2-x^2))},\ -a< x < a (ii) tan^(-1){sqrt((a-x)/(a+x))},\ -a< x < a

Express each of the following ratios in simplest form : 1 (2)/(3) : 2 (1)/(2) : 1(3)/(4)