Question

How do you prove `cos[(pi/2)-x]/sin[(pi/2)-x]=tanx`?

Answer 1

It's because `cos(pi/2 -x) = sin(x)`, and `sin(pi/2 -x) = cos(x)`

Explanation:

You need to use two simple trigonometric equality, namely

`{ (cos(pi/2 -x) = sin(x)), (sin(pi/2 -x) = cos(x)):}`

Using these two equalities, your expression becomes

`sin(x)/cos(x)`, which is exactly the definition of `tan(x)`