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Use the sum-to-product identity for sine.

April 22, 2026Mathematics

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Answer

2 \sin 40^\circ \cos 10^\circ

3 steps

Use the sum-to-product identity for sine.
The identity is $\sin A + \sin B = 2 \sin \left(\frac{A+B}{2}\right) \cos \left(\frac{A-B}{2}\right)$ .
Substitute $A = 50^\circ$ and $B = 30^\circ$ into the identity.
$\sin 50^\circ + \sin 30^\circ = 2 \sin \left(\frac{50^\circ+30^\circ}{2}\right) \cos \left(\frac{50^\circ-30^\circ}{2}\right)$
Simplify the angles.
$\sin 50^\circ + \sin 30^\circ = 2 \sin \left(\frac{80^\circ}{2}\right) \cos \left(\frac{20^\circ}{2}\right)$ $\sin 50^\circ + \sin 30^\circ = 2 \sin 40^\circ \cos 10^\circ$
The expression as a product is:
$2 \sin 40^\circ \cos 10^\circ$