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

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

Prove the following identities: sin^4A+cos^4A=1-2sin^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: cot^4A-1=cos e c^4A-2cos e c^2A

Prove the following identities: sin^(4)A+cos^(4)A=1-2sin^(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^(6)A+cos^(6)A=1-3sin^(2)A cos^(2)A

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

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