JEE Math Practice Question

The value of k for which the function $$f\left( x \right) = \left\{ {\begin{matrix} {{{\left( {{4 \over 5}} \right)}^{{{\tan \,4x} \over {\tan \,5x}}}}\,\,,} & {0 < x < {\pi \over 2}} \\ {k + {2 \over 5}\,\,\,,} & {x = {\pi \over 2}} \\ \end{matrix} } \right.$$ is continuous at x = $${\pi \over 2},$$ is :

1. A.$${{17} \over {20}}$$
2. B.$${{2} \over {5}}$$
3. C.$${{3} \over {5}}$$
4. D.$$-$$ $${{2} \over {5}}$$