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