Answer:
Option A
Explanation:
Given : $u_{n}\int_{0}^{\pi/4}\tan^{n}\theta d\theta$
= $\int_{0}^{\pi/4}\tan^{2}\theta \tan^{n-2}\theta d\theta$
= $\int_{0}^{\pi/4}(\sec^{2}\theta-1) \tan^{n-2}\theta d\theta$
= $\int_{0}^{\pi/4}\sec^{2}\theta \tan^{n-2}\theta d\theta$ - $\int_{0}^{\pi/4}\tan^{n-2}\theta d\theta$
= $\int_{0}^{\pi/4}(\sec^{2}\theta) \tan^{n-2}\theta d\theta$ - un-2
un + un-2 = $\int_{0}^{\pi/4}\sec^{2}\theta\tan^{n-2}\theta d\theta$
= $\frac{\tan^{n-1}\theta}{n-1}\mid_0^\frac{\pi}{4}$ = $\frac{1}{n-1}$
