Find the limits for two triangle functions by using fundamental limit. [closed]

Question

I occurred two problems about finding limit today. The questions ask finding limit by using the fundamental limit.

$$\lim_{x \to 0} \frac{\sin x }{x } = 1$$

The questions will show below as a picture. (Sorry I am really not familiar with math format)

enter image description here

Here are the limits.

$$\lim_{x \to 0} \frac{x \tan(x^2)}{\cos(5x)\sin^3(3x)} $$

$$\lim_{x \to \pi/2} \frac{\cos^2(x)}{(2x-\pi)\tan(2x)} $$

Answer 1

Here is a start on what you need:

$\tan(x) =\frac{\sin(x)}{\cos(x)} $

$\lim_{x \to 0} \cos(x) =1 $

$\sin(\pi/2-x) =\cos(x) $

$\cos(\pi/2-x) =\sin(x) $