# Product To Sum Identities

## Reference > Algebra: Trigonometric Identities

 Description$$\cos{x}\cos{y} = \frac{1}{2}(\cos{(x+y)}+\cos{(x-y)})$$ $$\sin{x}\sin{y} = \frac{1}{2}(\cos{(x-y)}-\cos{(x+y)})$$ $$\sin{x}\cos{y} = \frac{1}{2}(\sin{(x+y)}+\cos{(x-y)})$$
 Examples${x}^{3}+6{x}^{2}+12x+8$1 Rewrite it in the form $${a}^{3}+3{a}^{2}b+3a{b}^{2}+{b}^{3}$$, where $$a=x$$ and $$b=2$$.${x}^{3}+3{x}^{2}(2)+3(x)\times {2}^{2}+{2}^{3}$2 Use Cube of Sum: $${(a+b)}^{3}={a}^{3}+3{a}^{2}b+3a{b}^{2}+{b}^{3}$$.${(x+2)}^{3}$Done(x+2)^3