Expand the Trigonometric Expression sin(a+b)+sin(a-b)

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Trigonometry

$\sin (a + b) + \sin (a - b)$

Simplify each term.

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Apply the sum of angles identity.

$\sin (a) \cos (b) + \cos (a) \sin (b) + \sin (a - b)$

Apply the difference of angles identity.

$\sin (a) \cos (b) + \cos (a) \sin (b) + \sin (a) \cos (b) - \cos (a) \sin (b)$

Simplify by adding terms.

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Combine the opposite terms in $\sin (a) \cos (b) + \cos (a) \sin (b) + \sin (a) \cos (b) - \cos (a) \sin (b)$ .

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Subtract $\cos (a) \sin (b)$ from $\cos (a) \sin (b)$ .

$\sin (a) \cos (b) + \sin (a) \cos (b) + 0$

Add $\sin (a) \cos (b) + \sin (a) \cos (b)$ and $0$ .

$\sin (a) \cos (b) + \sin (a) \cos (b)$

Add $\sin (a) \cos (b)$ and $\sin (a) \cos (b)$ .

$2 \sin (a) \cos (b)$

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