Question

What is the domain of function `f(x)={sinx}/{tanx}`?

Answer 1

Domain of the function`f(x) = sin x/tan x`

Explanation:

The common period, or domain, of a trig function F(x), containing 2 trig functions f(x) and g(x), should be the least multiple of the 2 periods.
Here, the period of sin x is `2pi`, and the period of tan x is `pi`, therefor, their common period is `2pi`.

Answer 2

The domain of `f` is all real numbers except integer multiples of `pi/2`. All real `x` with `x != k pi/2` with `k` an integer.

Explanation:

Tangent in not defined for odd multiples of `pi/2` (where the cosine is `0`.)

Tangent is `0`, at integer multiples of `pi`, so this `f` is not defined for integer multiples of `pi`.

Since the even multiples of `pi/2` are the integer multiples of `pi`
and, since we have also excluded odd multiples of `pi/2`,

the domain excludes all integer multiples of `pi/2`.(both even and odd)

Note
For all `x` in the domain, this `f (x)` simplifies to `f(x) = cosx`.