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  4. If In=∫ limits0(π/4) tan n x d x where n is positive integer then I10+I8 is equal to

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Q. If $I_{n}=\int\limits_{0}^{\frac{\pi}{4}} \tan ^{n} x\, d x$ where $n$ is positive integer then $I_{10}+I_{8}$ is equal to

KCETKCET 2021Integrals

Solution:

$I _{ n }+ I _{ n -2}=\frac{1}{ n -1}$