2019-II-22

Ans: B
Since $ABCD$ is a rectangle, then $AB = CD$ (property of rectangle).

In $\Delta ABC$,

$\begin{array}{rcl}
\cos \alpha & = & \dfrac{AB}{AC} \\
AC & = & \dfrac{AB}{\cos \alpha}
\end{array}$

In $\Delta CDE$,

$\begin{array}{rcl}
\cos \beta & = & \dfrac{CD}{CE} \\
CE & = & \dfrac{CD}{\cos \beta}
\end{array}$

Hence, we have

$\begin{array}{rcl}
\dfrac{CE}{AC} & = & \dfrac{CD}{\cos \beta} \div \dfrac{AB}{\cos \alpha} \\
\dfrac{CE}{AC} & = & \dfrac{AB}{\cos \beta} \times \dfrac{\cos \alpha}{AB} \\
\dfrac{CE}{AC} & = & \dfrac{\cos \alpha}{\cos \beta}
\end{array}$