## hawkfalcon 2 years ago How do I simplify this expression?

1. hawkfalcon

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

2. jim_thompson5910

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

3. hawkfalcon

Thank you both, that makes sense:)

4. jim_thompson5910

np