Question 62
The real-valued function $f$ satisfies
$$
f(\tan 2x) = \tan^4 x + \cot^4 x
$$
for all real $x$. Prove that, for all real $x$,
$$
f(\sin x) + f(\cos x) \ge 196.
$$
$$
f(\tan 2x) = \tan^4 x + \cot^4 x
$$
for all real $x$. Prove that, for all real $x$,
$$
f(\sin x) + f(\cos x) \ge 196.
$$