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If I_n is the integral of tan^n x from 0 to pi/4, find I_(n+2) + I_n

The same question, asked 2 times: 14 May 2024 S2*, 20 Apr 2026 S2. Every wording below, oldest first.

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  1. Question 1

    14 May 2024 S2

    142
    If In=∫0π/4tan⁡nθ dθI_n = \int_0^{\pi/4} \tan^n\theta\,d\theta, then I12+I10I_{12} + I_{10} =

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  2. Question 2

    20 Apr 2026 S2

    84
    If In=∫0π/4tan⁡nx dx,n∈NI_n = \int_0^{\pi/4}\tan^n x\,dx, n \in N then In+2+InI_{n+2} + I_n is equal to

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