Question

If
$$sin(x)=2cos(x)$$
Find :
$$cos2x$$
.
.
1#

If
$$sin(x)=2cos(x)$$
So :
$$tan(x)=2$$
So
$$tan(2x)=\frac{2tan(x)}{1-tan^2(x)}=\frac{-4}{3}$$
So as shown in the  figure below :
$$cos(2x)=\frac{3}{5}$$

Prove !!

Prove that :
$$0!=1$$

By starting from :

$$x!=x(x-1)!$$
Then
$$1!=1(1-1)!$$

$$1!=0!$$
finally ,,
$$1=0!$$