Ellie Goulding - Lights (2010 Album Cover).rar

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Ellie Goulding - Lights (2010 Album Cover).rar
Ellie Goulding - Lights (2010 Album Cover)    . If you are looking for the complete Ellie Goulding - Lights (2010 Album Cover) album,then you are at the right site. Here you will get all of the albums in DRM-free mp3 .
Ellie Goulding - Lights (2010 Album Cover).rar
Ellie Goulding - Lights (2010 Album Cover).rar

We have a collection of 91 official Ellie Goulding - Lights (2010 Album Cover) covers, presented in high resolution.Q:

How to prove this identity without using property of exponents?

Could someone please prove this identity?
$$\dfrac\sin(x)x = \left(1 - \cos(x)\right)\cdot\left(1 + \cos(x)\right) + \sin(x)\cdot\left(2\cos(x)\right)$$
How to prove this without using property of exponents.
Thanks

A:

$$\frac\sin(x)x=\frace^ix-e^ -ix2i=\frac(e^ix+e^ -ix)-(e^ -ix+e^ix)2i=$$
$$=\frace^ix-e^ -ix2i\frace^ix+e^ -ixe^ix+e^ -ix+\frace^ -ix-e^ix2i\frace^ix+e^ -ixe^ -ix+e^ix=$$
$$=\frac1-\cos(2x)2i+\frac\cos(2x)2i=$$
$$=\left(\frac12i-\cos(2x)\right)+\left(\frac12i+\cos(2x)\right)=$$
$$=\left(1-\cos(2x)\right)\left(1+\cos(2x)\right)+\sin(2x)\left(2\cos(2x)\right)$$

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Ellie Goulding - Lights (2010 Album Cover).rar

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Ellie Goulding - Lights (2010 Album Cover).rar

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