Question

hii..
$\sec \alpha (1 - \sin \alpha)( \sec \alpha + \tan \alpha ) = 1 \\ \\ prove \: it....$

Answer 1

hope this helps you ☺☺

Answer 2

Hey dear! I'm replacing alpha with '¢'

Ques :- PT .Sec ¢ (1 - sin ¢) (sec ¢ + tan ¢) = 1

LHS = sec ¢ (1 - sin ¢) (sec ¢ + tan ¢)

= (1/ cos ¢) ( 1 - sin ¢) (sec ¢ + tan ¢)

= {(1/ cos ¢) - ( sin ¢ / cos ¢)} {( 1/ cos ¢) + ( sin ¢ / cos ¢)}

= {( 1 - sin ¢) / cos ¢} {( 1 + sin ¢) / cos ¢}

( Use the identity ----> (a + b) ( a - b) = a² - b²

= ( 1 - sin² ¢) / cos² ¢

= cos² ¢ / cos² ¢

= 1 <= RHS

Hence proved.

Hope it helps! ^^