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

2 Answers
Mar 31, 2018

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.

Mar 31, 2018

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