Why does sin (x) / cos (x) = tan (x) ?

Sin (x) = o/h

cos (x) = a/h

tan (x) = o/a

If we try to use o/h (sin) and a/h (cos) to write o/a (tan), it would look like:

o x h = o

h a a

o/h is sin

h/a is the inverse of cos (which is a/h)

when you divide by a fraction, you multiply by the inverse of the fraction. In this case, o/h (sin) is being divided by a/h (cos)

therefore sin (x) / cos (x) = tan (x)

another way of thinking about it is looking at a triangle.

To get the side opposite the angle x, you use sin (x)

to get the side adjacent to the angle x, you use cos (x)

because tan (x) = side opposite angle x / side adjacent angle x, then:

tan (x) = sin (x) / cos (x)