Prove the following identities :
tan2 A - sin2 A = tan2 A. sin2 A
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sec2 A + cosec2 A = sec2 A . cosec2 A
(cosec A + sin A)(cosec A - sin A) = cot2 A + cos2 A
(cos A + sin A)2 + (cos A - sin A)2 = 2