# Thread: Trig Identities - Simplifying

1. ## Trig Identities - Simplifying

(Cot^2 X)/(1+ Csc X) + Sin X * Csc X

It's been a while on this stuff, but what does this simplify down to?

2. Originally Posted by gregmosu
(Cot^2 X)/(1+ Csc X) + Sin X * Csc X

It's been a while on this stuff, but what does this simplify down to?
Change everything to sin and cos

Spoiler:
$\frac{\cos ^2 x}{\sin ^2 x (1+ \frac{1}{\sin x})}+1$

$1+\frac{1}{\sin(x)} = \frac{\sin (x) + 1}{\sin(x)}$

$\frac{\cos ^2 x}{\sin x+ \sin ^2x}+1 = \frac{\cos^2 x + \sin x + \sin ^2x}{\sin x + \sin ^2 x} = \frac{\sin x}{\sin x(1+\sin x)}$
$\frac{1}{1+\sin x}$

3. Originally Posted by gregmosu
(Cot^2 X)/(1+ Csc X) + Sin X * Csc X

It's been a while on this stuff, but what does this simplify down to?
Can you show us your work so far, then we can help where you get stuck.

4. Here's my work one step at a time.

1) (Cot^2 X)/(1 + Csc X) + (1/Csc X) * Csc X

2) (Cot^2 X)/(1 + Csc X) + 1

3) (Csc^2 X - 1)/(1 + Csc X) + 1

Is this right so far?

Actually after taking a second look, it appears that this would simplify to Csc X.

5. Originally Posted by gregmosu
Here's my work one step at a time.

1) (Cot^2 X)/(1 + Csc X) + (1/Csc X) * Csc X

2) (Cot^2 X)/(1 + Csc X) + 1

3) (Csc^2 X - 1)/(1 + Csc X) + 1

Is this right so far?
Yes, that's fine.

Next -- use the difference of two squares on $\csc ^2(x) - 1$

edit: you'd be right -- it does equal csc(x)