Question

1. sec A (1 – sin A) (sec A + tan A) = 1

Answer 1

Answer:

L.H.S. =  sec A (1 – sin A) (sec A + tan A)  

  = 1/ cos A * ( 1-sin A ) ( 1/ cosA + sin A /cos A)

 = 1/ cos A * (1 -sin A){  ( 1+ sin A ) /cos A }  ----> taking LCM

 = 1/ cos A  * ( 1- sin^2  A ) / cos A   ---> a^2 - b^2 =( a+b)(a-b)

= cos ^2 A / cos^2 A

= 1

R.H.S

Proved.