Prove why Tan equals sin/cos?

In a right triangle ABC, whose right angle is A, the
tangent ratio of the angle B is the opposite leg over the adjacent
leg.

tan B =
opposite/adjacent

We'll express the sine and cosine
functions of the angle B:

sin B = opposite/hypotenuse
=> opposite = hypotenuse*sin B

cos B =
adjacent/hypotenuse => adjacent = hypotenuse*cos
B

We'll re-write the tangent
ratio:

tan B = opposite/adjacent <= > tan B =
hypotenuse*sin B/hypotenuse*cos B

We'll reduce
hypotenuse:

tan B = sin B/cos
B

Therefore, in a right angle triangle, the
tangent ratio of an angle, except the right angle, is: tan `alpha` = sin `alpha` / cos
`alpha` .