In the interval $(0, \pi / 2)$, the function $f(x)=\tan ^n x+\cot ^n x$ attains

the minimum value which is independent of n a minimum value which is a function of n the minimum value of 1 none of these

the minimum value which is independent of n

We have, $f(x) =\tan ^n x+\cot ^n x$ $\Rightarrow f(x) =\left(\tan ^{n / 2} x-\cot ^{n / 2} x\right)^2+2 \geq 2$ Clearly, f(x) attains the minimum value 2 when $\tan ^{n / 2} x-\cot ^{n / 2} x=0$ i.e. $x=\frac{\pi}{4}$