Question

What is sin/cos + cos/sin, and why?

Answer 1

The problem here is "how far back do we need to go?" when we try to explain "why?"

Assuming that the following identities are known:
`sin^2(x)+cos^2(x) = 1`
and
`sin(2x) = 2sin(x)cos(x)`

`(sin(x))/(cos(x)) + (cos(x))/(sin(x))`

`= (sin(x))/(cos(x)) * (sin(x))/(sin(x)) + (cos(x))/(sin(x)) * (cos(x))/(cos(x))`

`= (sin^2(x)+cos^2(x))/cos(x)sin(x)`

`= 1/(cos(x)sin(x))`

or
`= 2/sin(2x)`