Question

What is the expression that remains when we simplify $(secA+tanA)(1-sinA)?$

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

Answer 1

The correct option is D cos A

$(secA+tanA)(1-sinA)$

= $(\frac{1}{cosA}+\frac{sinA}{cosA})(1-sinA)$
= $\frac{1+sinA}{cosA}\times (1-sinA)$
= $\frac{1-si{n}^{2}A}{cosA}$
= $\frac{co{s}^{2}A}{cosA}=cosA$