If `I_n=int_0^(pi//4)tan^("n")x dx` , prove that `I_n+I_(n-2)=1/(n-1)dot`

Explanation

To prove that \( I_n + I_{n-2} = \frac{1}{n-1} \), where \( I_n = \int_0^{\frac{\pi}{4}} \tan^n x \, dx \), we will follow these steps:

### Step 1: Write down the expressions for \( I_n \) and \( I_{n-2} \)

We have:
\[ I_n = \int_0^{\frac{\pi}{4}} \tan^n x \, dx \]
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