Question

Choose the correct option. Justify your choice
$(\sec A+\tan A)(1-\sin A)=$

• A. $\sec A$
• B. $\sin A$
• C. $cosecA$
• D. $\cos A$

Answer 1

The correct option is D $\cos A$

The value of $(\sec A+\tan A)(1-\sin A)$

$(\frac{1}{\cos A}+\frac{\sin A}{\cos A})(1-\sin A)$

$=\left(\frac{1+\sin A}{\cos A}\right)(1-\sin A)$

$=\frac{1-{\sin }^{2}A}{\cos A}=\frac{{\cos }^{2}A}{\cos A}=\cos A$