trigonometry - Solving complicated trigonometric limits

Can someone help me solve this limits? I know how to solve basic trigonometric limits, but this is too advanced for me. I know that i should start by writing that $\tan x=\sin x/\cos x$. Some instructions after that?

$$\Large\lim_{x\to\frac{\pi}{4}}(\tan x)^{\tan2x}$$

$$\Large\lim_{x\to\frac{\pi}{2}}(\tan x)^{\sin x}$$