Question

(1 - cos A) (1 + sec A) = tan A sin A​

Answer 1

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$(1 - cosa)(1 + seca) \\ = (1 - cosa)( \frac{1 + cosa}{cosa} ) \\ = \frac{1 - {cos}^{2} a}{cosa} \\ = \frac{ {sin}^{2} a}{cosa} \\ = \frac{sina}{cosa} cosa \\ = tana \: sina$

Answer 2

Formula used :

$1 - {cos}^{2} a = {sin}^{2} a$

Refer the attachment ✔️