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

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: sin^4A-cos^4A=sin^2A-cos^2A=2sin^2A-1=1-2cos^2A

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

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

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

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

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