Question

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

Answer 1

Step-by-step explanation:

$seca(1 - sina)(seca + tana) = 1 \\ </p><p>L. H. S</p><p>\frac{1}{cosa} (1 - sina)( \frac{1}{cosa} - \frac{sina}{cosa} ) \\= \frac{1}{cosa} (1 - sina) ( \frac{1 - sina}{cosa} ) \\ = \frac{1}{ {cos}^{2} a} ( {1}^{2} - {sin}^{2} a) \\ = \frac{ {cos}^{2}a }{ {cos}^{2} a} = 1 \\ l.h.s = r.h.s$