question_answer

The value of K for which the function\[f(x)=\left\{ \begin{matrix}    {{\left( \frac{4}{5} \right)}^{\frac{\tan 4x}{\tan 5x}}}, & 0<x<\frac{\pi }{2}  \\    k+\frac{2}{5} & x=\frac{\pi }{2}  \\ \end{matrix} \right.\] is continuous at \[x=\frac{\pi }{2},\] is        [JEE Online 09-04-2017]

A)  \[\frac{2}{5}\]                                  

B)  \[-\frac{2}{5}\]

C)  \[\frac{17}{20}\]                                             

D)  \[\frac{3}{5}\]