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# How do you prove sin (x + y + z) = sin x cos y cos z + cos x sin y cos z + cos x cos y sin z - sin x sin y sin z?

How do you prove sin (x + y + z) = sin x cos y cos z + cos x sin y cos z + cos x cos y sin z - sin x sin y sin z?

#### Homework Answers

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#### Explanation:

Use Formulas: $\sin \left(A + B\right) = \sin A \cos B + \cos A \sin B$

$\cos \left(A + B\right) = \cos A \cos B - \sin A \sin B$

$A = x + y , B = z$

Left Side:$= \sin \left(\left(x + y\right) + z\right) = \sin \left(x + y\right) \cos z + \cos \left(x + y\right) \sin z$

$= \left(\sin x \cos y + \cos x \sin y\right) \cos z + \left(\cos x \cos y - \sin x \sin y\right) \sin z$

$= \sin x \cos y \cos z + \cos x \sin y \cos z + \cos x \cos y \sin z - \sin x \sin y \sin z$

$=$Right Side

answered by: Bdub
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