# Thread: Trig. Identities?

1. ## Trig. Identities?

[not sure if this would come under trig identities, (part B of this question is differentiation, but i'm not needing help with that)]

2. $\frac{\sin^3(x)+\cos^2(x)}{\sin^2(x)}$

$\frac{\sin^3(x)+(1-\sin^2(x))}{\sin^2(x)}$

$\sin(x)+\sin^{-2}(x)-1$

3. EDIT: How do you get -1?

4. you have the identity that:

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

so then $\cos^2(x)=1-\sin^2(x)$

so we then have:

$
\frac{\sin^3(x)}{\sin^2(x)}+\frac{1}{\sin^2(x)}{\c olor{blue} -\frac{\sin^2(x)}{\sin^2(x)}}$

so:

${\color{blue} - \frac{\sin^2(x)}{\sin^2(x)}=-1}$