[" Prove the following : "],[qquad (i)(sin A+cos A)^(2)+(sin A-cos A)^(2)=2]

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

Prove the following identity: (1-s in A cos A)/(cos A(sec A-cos ecA))(sin^(2)A-cos^(2))/(sin^(3)A+cos^(3)A)=sin A

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)

Prove the following identities : (cos A + sin A)^(2) + (cos A - sin A)^(2) = 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 (cos ^2A* sin^2 B)- (sin^2 A* cos ^2B)= cos^2 A- cos ^2B

Prove the following : cos^6A-sin^6A = cos2A(1-1/4 sin^2 2A)

Prove that [(1-sin A-cos A)^(2)=2(1-sin A)(1-cos A)]

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

Prove that (1+sin A+cos A)^(2)=2(1+sin A)(1+cos A)