Prove the following identities: `(sin^2A)/(cos^2A)+(cos^2A)/(sin^2A)=1/(sin^2Acos^2A)-2`

Prove the following identities: (sin^(2)A)/(cos^(2)A)+(cos^(2)A)/(sin^(2)A)=(1)/(sin^(2)A cos^(2)A)-2

Prove that (sin^2A)/(cos^2A)+(cos^2A)/(sin^2A)=1/(sin^2Acos^2A)-2 .

Prove the following identities: sin^4A+cos^4A=1-2sin^2Acos^2A

Prove the following identities: sin^6A+cos^6A=1-3sin^2Acos^2A

Prove the following identities: cos^8A-sin^8A=(1-2sin^2Acos^2A)(1-2sin^2A)

Prove the following identities: sin^4A-cos^4A=sin^2A-cos^2A=2sin^2A-1=1-2cos^2A

Prove the following identities: cos^4A-cos^2A=sin^4A-sin^2A

Prove the following identities : 1 - (sin^(2) A)/ (1 + cos A) = cos A

Prove the following identities : 1 - (sin^(2) A)/ (1 + cos A) = cos A

Prove the following identities: (sinA+cosA)/(sinA-cosA)+(sinA-cosA)/(sinA+cosA)=2/(sin^2A-cos^2A)=2/(2sin^2A-1)=2/(1-2cos^2A)