Question

How do I simplify this expression?

Answer 1

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

Answer 2

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


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


\[\Large \frac{1-(1+2\sin(x)\cos(x))}{2\sin(x)}\]


\[\Large \frac{1-1-2\sin(x)\cos(x)}{2\sin(x)}\]


\[\Large \frac{-2\sin(x)\cos(x)}{2\sin(x)}\]


\[\Large -\cos(x)\]

Answer 3

Thank you both, that makes sense:)

Answer 4

np