Question

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

Answer 1

Formulas used :

tan A = sin A / cos A

1 - sin²A = cos²A

cos A sec A = 1

Step-by-step explanation:

L.H.S

( sec A + tan A )( 1 - sin A )

⇒ ( sec A + sin A / cos A ) ( 1 - sin A )

⇒ [ ( sec A cos A + sin A ) / cos A  ] ( 1 - sin A )

⇒ [ 1 + sin A ] ( 1 - sin A ) / cos A

⇒ ( 1 - sin² A ) / cos A

⇒ cos² A / cos A

⇒ cos A [ Proved ]