(sec A + tan A) (1 – sin A) =

(A) sec A (B) sin A (C) cosec A (D) cos A

Dear Student

Option (D) is correct.

Justification:

We know that,
Sec A= 1/cos A
Tan A = sin A / cos A
Now,
substitute the above values in the given problem,
we get
(secA + tanA) (1 - sinA)

= (1/cos A + sin A/cos A) (1 - sinA) = (1+sin A/cos A) (1 - sinA)
= (1 - sin^2 A)/cos A
= cos^2 A/cos A
= cos A

Therefore, (secA + tanA) (1 - sinA) = cos A i.e Option (D)

Thanks