Trig Question

$$cos(x)/sin(x)=cos(x)/sin(x)$$

This is true for all values of x except ofcourse sinx cannot=0 so x cannot equal any integer multiple of pi

I think what you are asking about is the trig identity cos^2 (x) + sin^2(x) =1.

(What you have written just cancels down to 1=1.)

To see that the above identity is true,draw yourself a right-angled triangle,name the sides a,b and c with a hypotenuse,b adjacent and c opposite . Now define sin and cos from these and use Pythagoras. 

With regard to validity and domain,the identity is true for all angles.