Trigonometry Examples

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

Step 1

Simplify each term.

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Step 1.1

Apply the sum of angles identity.

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

Step 1.2

Apply the difference of angles identity.

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

Step 2

Simplify by adding terms.

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Step 2.1

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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Step 2.1.1

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

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

Step 2.1.2

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

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

Step 2.2

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

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