Prove that `(sec^(2)A)/(cos^(2)A)-(tan^(2)A)/(cot^(2)A)=1+2tan^(2)A`

(sec^2A)/(cos^2A)-(tan^2A)/(cot^2A)=1+2tan^2A

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

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

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

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

Prove :sin^(2)A cot^(2)A+cos^(2)A tan^(2)A=1

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

prove that ((1-tan A)/(1-cot A))^(2)=tan^(2)A

Prove that: sec^(2)(tan^(-1)2)+cos ec^(2)(cot^(-1)3)=15 and tan^(2)(sec^(-1)2)+cot^(2)(cos ec^(-1)3)=11

The expression cosec^(2)A cot^(2)A-sec^(2)A tan^(2)A-(cot^(2)A-tan^(2)A)(sec^(2)A cosec^(2)A-1) is equal to