Prove the following identity:
sec A (1 - sin A)(sec A + tan A) = 1
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(sin2 θ - 1) (tan2 θ + 1) + 1 = 0
cosec A (1 + cos A)(cosec A - cot A) = 1
(cosec θ - sin θ)(sec θ - cos θ)(tan θ + cot θ) = 1
(cosec A + sin A)(cosec A - sin A) = cot2 A + cos2 A