Question

What is the expression that remains when we simplify $(\sec A+\tan A)(1-\sin A)$?

• A. sin A
• B. 1 + sin A
• C. 1 + cos A
• D. cos A

Answer 1

The correct option is D cos A

$(\sec A+\tan A)(1-\sin A)$

= $(\frac{1}{\cos A}+\frac{\sin A}{\cos A})(1-\sin A)$
= $\frac{1+\sin A}{\cos A}\times (1-\sin A)$
= $\frac{1-{\sin }^{2}A}{\cos A}$
= $\frac{{\cos }^{2}A}{\cos A}=\cos A$