Question

How do you simplify `[cos(x+2pi)]/sinx`?

Answer 1

`cos(x+2pi)/sinx` = `cotx`

Explanation:

To simplify `cos(x+2pi)/sinx`, first one may note that adding `2pi` or its multiple, to a trigonometric ratio, does not change its value

i.e. `sin(x+2npi)=sinx` (for all `n`, where `n` is an integer), `cos(x+2npi)=cosx`, `tan(x+2npi)=tanx`, `cot(x+2npi)=cotx`, `sec(x+2npi)=secx` and `csc(x+2npi)=cscx`.

Hence, `cos(x+2pi)/sinx` = `cosx/sinx` or `cotx`.