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

Prove that (tan^(2)A-1)/(tan^(4)A-1)=cos^(2)A

i) Prove that: (1+tan^(2)A)/(1-tan^(2)A) xx (2 cos^(2) A-1)=1 ii) Prove that: (tantheta)/(1+cottheta)+(cottheta)/(1+tantheta) = "cosec"theta.sectheta-1

i) Prove that: (1+tan^(2)A)/(1-tan^(2)A) xx (2 cos^(2) A-1)=1 ii) Prove that: (tantheta)/(1+cottheta)+(cottheta)/(1+tantheta) = "cosec"theta.sectheta-1

Prove that cos2A=(1-tan^2 A)/(1+tan^2 A)

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

prove that (1-cos2A)/(1+cos2A)=tan^(2)A

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

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