If $I_n=\int\limits_0^{\pi/4}\tan^nx\, dx$ then $I_{2024} +I_{2026}$ is equal to:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → $\frac{1}{2025}$
$I_n=\displaystyle \int_{0}^{\pi/4} \tan^n x \, dx$
The known reduction identity is:
$I_n + I_{n+2} = \frac{1}{n+1}$
Substitute $n=2024$:
$I_{2024} + I_{2026} = \frac{1}{2025}$
$\frac{1}{2025}$