The value of $\frac{{e}^{-\frac{\pi }{4}}+{\int }_{0}^{\frac{\pi }{4}}{e}^{-x}{\tan }^{50}xdx}{{\int }_{0}^{\frac{\pi }{4}}{e}^{-x}\left({\tan }^{49}x+{\tan }^{51}x\right)dx}$ is [JEE Main 2023, 13 Apr (Shift 2)]

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The value of \(\frac{{e}^{-\frac{\pi }{4}}+{\int }_{0}^{\frac{\pi }{4}}{e}^{-x}{\tan }^{50}xdx}{{\int }_{0}^{\frac{\pi }…

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