(sec A + tan A) (1 − sin A) =
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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