Question:
$(\sec A+\tan A)(1-\sin A)=$
(a) sec A
(b) sin A
(c) cosec A
(d) cos A
Solution:
The given expression is $(\sec A+\tan A)(1-\sin A)$.
Simplifying the given expression, we have
$(\sec A+\tan A)(1-\sin A)$
$=\left(\frac{1}{\cos A}+\frac{\sin A}{\cos A}\right)(1-\sin A)$
$=\left(\frac{1+\sin A}{\cos A}\right) \times(1-\sin A)$
$=\frac{1-\sin ^{2} A}{\cos A}$
$=\frac{\cos ^{2} A}{\cos A}$
$=\cos A$
Therefore, the correct option is (d).
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