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

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}

Use Cube of Sum:

{(a+b)}^{3}={a}^{3}+3{a}^{2}b+3a{b}^{2}+{b}^{3}

{(x+2)}^{3}

Done