`(1- sin A - cos A)^2 = 2 (1-sin A) (1-cos A)`

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

Prove that : (1)/ (sin A - cos A) - (1)/ (sin A + cos A) = (2 cos 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)

(i) (1-cos A)/(sin A)=(sin A)/(1+cos A)

Show that : sin^8 A-cos^8 A = (sin^2 A - cos^2 A) (1-2 sin^2 A*cos^2 A)

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

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

Prove that : (tan A + (1)/ (cos A))^(2) + (tan A - (1)/ (cos A))^(2) = 2 ((1 + sin^(2) A)/ (1 - sin^(2) A))

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

Prove that : (1+sin 2A)/(cos 2A) = (cos A + sin A)/(cos A - sin A) = tan (pi/4 + A)