Because cos 90 = 0 (if you put in calculator) and will kill off the - 2ab cos C.

You will learn in A Maths that cos 90 is 0.

In short, the cosine rule works for any angle from 0 to 180, even for right angled triangles.

Because for right angled triangles, C = 90 and the formula reduces to the Pyth Thm.

how about a^2 + b^2 > c^2 and a^2 + b^2 < c^2 tho

It has to depend on the angle. If an angle is acute, then cos angle is positive correct? This will cause -2ab sin C to become a negative value, so that

a2 + b2 - 2ab sin C, which is the same as c2,

becomes clearly smaller than

a2 + b2.

So, for the case acute angle, c2 < a2 + b2.

You can make a similar conclusion for obtuse angle.