`Tan Q /(1-cotQ)+cotQ/(1-tanQ )=1+secQcosecQ`

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

If (tan^(3)A)/(1+tan^(2)A)+(cot^(3)A)/(1+cot^(2)A)=p secA"cosec"A+q sinA cosA , then :

tan^(-1)(-1)=-tan^(-1)(1)

Prove that : 2 tan^(-1) (cosec tan^(-1) x - tan cot^(-1) x) = tan^(-1) x

4 tan^(-1)(1/5)-tan^(-1)(1/239) is equal to

tan^(-1)(1/2)+tan^(-1)(1/3) is equal to

Prove that: tan^(-1) (1/2tan2A) + tan^(-1) (cotA) + tan^(-1) (cot^3A) =0

If (tan^(-1)x)^(3)+(tan^(-1)y)^(3)=1-3tan^(-1)x.tan^(-1)y . Then which of the following may be true (a) (x+y)/(tan1)=-2 (b) (tan^(-1)x)/(1-tan^(-1)y)=2 (c) (tan^(-1)x)/(1-tan^(-1)y)=2 (d) (x+y)/(cot1)=1

Prove that (1+ tan 1^@ ) (1+ tan 2^@ )...(1+ tan 45º )= 2^23

If tan^(-1) x+tan^(-1)y+tan^(-1)z=pi/2 then prove that yz+zx+xy=1