The value of $$\frac{e^{-\frac{\pi}{4}} + \int_0^{\frac{\pi}{4}} e^{-x}\tan^{50}x \ dx}{\int_0^{\frac{\pi}{4}} e^{-x}(\tan^{49}x + \tan^{51}x) \ dx}$$

A

$$51$$

B

$$50$$

C

$$25$$

D

$$49$$