Trig expression. I have no idea how to simplify past the first part.

[barren hornet]

[median path]

Rule 1 of trigonometry is to rewrite everything in sine and cosine.

[median path]

Okay, you did way more than Rule 1 there.

I don't recognize that expression at all.

[barren hornet]

Ight I'll back track sorry

[median path]

Oh, I didn't notice that.

We can just focus on simplifying cos(x)/(1 + csc(x)). We're multiplying it by 1.

But, for the sake of completeness. Rule 1 of complex fractions is to not have them.

[barren hornet]

I see

[median path]

So how would you fix these complex fractions?

[barren hornet]

Changing them to their reciprocal identities?

[median path]

...no.

[barren hornet]

😦

[median path]

That would just be undoing the one step we just did.

This is basic algebra.

...you multiply the top and bottom of the big fraction by the denominator of the little fraction.

[median path]

...what?

What I meant was to multiply it by sin(x)/sin(x). Which gets you the same result, but I can't follow your work closely enough to tell if you made an algebra mistake.

[median path]

Oh! I get it now!

The instructions aren't to simplify cos(x)/(1 + csc(x)) * (1 - csc(x))/(1 - csc(x)), they're to simplify cos(x)/(1 + csc(x)) by multiplying it by (1 - csc(x))/(1 - csc(x)).

[uncut roost]

Yes, this can be simplified to 2 uses of trig functions. Hint:

$1 + \cot^2x = \csc^2x$

[wet knoll]

TruthNerds

[uncut roost]

This follows directly (by dividing by the square of the sine) from:

$\sin^2x + \cos^2x = 1$