Question

On simplifying the expression $(\sec A+\tan A)(1-\sin A)$, we get

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

Answer 1

The correct option is D cos A

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

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