Question

The expression $E=\frac{cotA-cosA}{cotA+cosA}$ is the same in value in which of the following expressions?

• A. (1 - cosecA)/(1 + cosecA)
• B. (1 - cotA)/(1 + cotA)
• C. (1 - sinA)/(1 + sinA)
• D. (1 - sinA)/cosA
• E. (cosA + secA)/(cosA - secA)

Answer 1

The correct option is C

(1 - sinA)/(1 + sinA)

$\begin{array}{c}E=\frac{\frac{cosA}{sinA}-cosA}{\frac{cosA}{sinA}+cosA}\\ =\frac{cosA\left(1-sinA\right)}{cosA\left(1+sinA\right)}\\ =\frac{1-sinA}{1+sinA}=\frac{cosecA-1}{cosecA+1}\end{array}$