Question:
(sec A + tan A) (1 − sin A) = ?
(a) sin A
(b) cos A
(c) sec A
(d) cosec A
Solution:
(b) cos A
$(\sec A+\tan A)(1-\sin A)$
$=\left(\frac{1}{\cos A}+\frac{\sin A}{\cos A}\right)(1-\sin A)$
$=\left(\frac{1+\sin A}{\cos A}\right)(1-\sin A)$
$=\left(\frac{1-\sin ^{2} A}{\cos A}\right)$
$=\left(\frac{\cos ^{2} A}{\cos A}\right)$
$=\cos A$