## Trigonometry (11th Edition) Clone

$$2\sin58^\circ\cos102^\circ=\sin160^\circ-\sin44^\circ$$
$$A=2\sin58^\circ\cos102^\circ$$ The product-to-sum identity that will be applied here is $$\sin X\cos Y=\frac{1}{2}[\sin(X+Y)+\sin(X-Y)]$$ Therefore, A would be $$A=2\times\frac{1}{2}[\sin(58^\circ+102^\circ)+\sin(58^\circ-102^\circ)]$$ $$A=\sin160^\circ+\sin(-44^\circ)$$ We know that $\sin(-X)=-\sin X$. That means $$A=\sin160^\circ-\sin44^\circ$$