Answer
$$2\cos85^\circ\sin140^\circ=\sin225^\circ+\sin55^\circ$$
Work Step by Step
$$A=2\cos85^\circ\sin140^\circ$$
The product-to-sum identity that will be applied here is $$\cos X\sin Y=\frac{1}{2}[\sin(X+Y)-\sin(X-Y)]$$
Therefore, A would be $$A=2\times\frac{1}{2}[\sin(85^\circ+140^\circ)-\sin(85^\circ-140^\circ)]$$ $$A=\sin225^\circ-\sin(-55^\circ)$$
We know that $\sin(-X)=-\sin X$. That means $$A=\sin225^\circ+\sin55^\circ$$
