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

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

(sin^4A-cos^4A)/(sin^2A-cos^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

cos^6A-sin^6A=cos2A(1-1/4sin^2 2A)

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)

If (cos^4A)/(cos^2B)+(sin^4A)/(sin^2B)=1 then prove that (i)sin^4A+sin^4B=2sin^2Asin^2B (ii)(cos^4B)/(cos^2A)+(sin^4B)/(sin^2A)=1

(cos3A-cos A)/(sin3A-sin A)+(cos2A-cos4A)/(sin4A-sin2A)=(sin A)/(cos2A cos3A)

cos^(6)A+sin^(6)A=1-3/4sin^(2)(2A)

cos^(6)A+sin^(6)A=1-3/4sin^(2)(2A)

If (cos^4A)/(cos^2B)+(sin^4A)/(sin^2B)=1 , then prove that (i) sin^4A+sin^4B=2 sin^2Asin^2B (ii) (cos^4B)/(cos^2A)+(sin^4B)/(sin^2A)=1