Question

Simplify:
(SecA + TanA) ( 1 - SinA)

Answer 1

Step-by-step explanation:

$( \sec \: A \: + \: \tan \: A \: )(1 - \: sin \: A ) \\ = (\frac{1}{cos \: A } + \frac{sin \: A}{cos \: A } )(1 - \: sin \: A ) \: \\ = \frac{(1 + \: sin \: A )(1 - \: sin \: A )}{cos \: A} \\ = \frac{1 - {sin}^{2}A }{cos \: A} \: \\ = \frac{ { {cos}^{2} A} }{cos \: A} \: \\ = cos \: A \:$