Question

Can we prove this is an identity? Sin(x) Cot(x)=Cos(x)

Answer 1

Yes. See below.

Explanation:

It's best to get this in a form involving only sine and cosine.

Recall that `cotx=cosx/sinx`. Applying this to the problem yields:

`cancelsinx(cosx/cancelsinx)=cosx`

`cosx=cosx`

So, yes, it is an identity.

Answer 2

Please see below.

Explanation:

.

`sinxcotx=cosx`

`cotx=cosx/sinx`

Let's plug it in:

`sinxcotx=sinx(cosx/sinx)=cancelcolor(red)sinx(cosx/cancelcolor(red)sinx)`

`sinxcotx=cosx`