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` .