Show that: `1/(sec A-tan A) - 1/(cos A) = 1/(cos A) - 1/(sec A + tan A)`

Show that (i) sin^(8)A-cos^(8)A=(sin^(2)A-cos^(2)A)(1-2sin^(2)A.cos^(2)A) (ii) (1)/(sec A-tan A)-(1)/(cos A)=(1)/(cos A)-(1)/(sec A + tan A)

Prove that : (cosec A - sin A) (sec A - cos A) sec^(2) A = tan A

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

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

Prove that : sin A (1 + tan A) + cos A (1 + cot A) = sec A + cosec A.

Prove that : (tan A + cot A) (cosec A - sin A) (sec A - cos A) = 1

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

Prove that : (tan A)/ (1 - cot A) + (cot A)/ (1 - tan A) = sec A cosec A + 1

Prove that: (tanA+ sec A-1)/(tan A-secA+1)=(cosA)/(1-sinA)

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