I'm trying to typeset some trig identity manipulation but when I produce the PDF the line is cut off. I am not sure how to get it to display across multiple lines. I did look at the other similar posts but I couldn't figure it out.
\begin{align*}
2 \sin\left(\frac{x+y}{2}\right) \cos\left(\frac{x-y}{2}\right) &= 2\left(\sin\left(\frac{x}{2}\right)\cos\left(\frac{y}{2}\right) + \sin\left(\frac{y}{2}\right)\cos\left(\frac{x}{2}\right)\right)\left(\cos\left(\frac{x}{2}\right)\cos\frac{y}{\
2} + \sin\left(\frac{x}{2}\right)\sin\left(\frac{y}{2}\right)\right)\\
&= 2\biggl(\sin(\frac{x}{2})\cos(\frac{x}{2})\cos^{2}(\frac{y}{2}) + \sin^{2}(\frac{x}{2})\cos(\frac{y}{2})\sin(\frac{y}{2}) + \sin(\frac{y}{2})\cos(\frac{y}{2})\cos^{2}(\frac{x}{2}) \notag \\
&= \sin^{2}(\frac{y}{2})\cos(\frac{x}{2})\sin(\frac{x}{2}\biggr) \notag \\
&= 2\sin(\frac{x}{2})\cos(\frac{x}{2})\cos^{2}(\frac{y}{2}) + 2\sin^{2}(\frac{x}{2})\cos(\frac{y}{2})\sin(\frac{y}{2}) + 2\sin(\frac{y}{2})\cos(\frac{y}{2})\cos^{2}(\frac{x}{2}) \notag \\
&= 2\sin^{2}(\frac{y}{2})\cos(\frac{x}{2})\sin(\frac{x}{2}) \notag \\
&= \sin(x)\cos^{2}(\frac{y}{2}) + \sin(x)\sin^{2}(\frac{y}{2}) + \sin(y)\cos^{2}(\frac{x}{2}) + \sin(y)\sin^{2}(\frac{x}{2}) \\
&= (\sin(x))(\cos^{2}(\frac{y}{2} + \sin^{2}(\frac{y}{2})) + \sin(y)(\cos^{2}(\frac{x}{2} + \sin^{2}(\frac{x}{2}) \\
&= \sin (x)+ \sin (y)
\end{align*}
What is the best way to code this so the line is not cut off?
\sin(a+b)+\sin(a-b)=2\sin a\cos b
and replacea+b
withx
anda-b
withy
.