Sine plus Sine/Examples/Sine 40 plus Sine 60
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Example of Use of Sine plus Sine
- $\sin 40 \degrees + \sin 60 \degrees = 2 \sin 50 \degrees \cos 10 \degrees$
Proof
| \(\ds \sin 40 \degrees + \sin 60 \degrees\) | \(=\) | \(\ds 2 \map \sin {\dfrac { {40 \degrees} + {60 \degrees} } 2} \map \cos {\dfrac { {40 \degrees} - {60 \degrees} } 2}\) | Sine plus Sine | |||||||||||
| \(\ds \) | \(=\) | \(\ds 2 \sin 50 \degrees \map \cos {-10 \degrees}\) | evaluating | |||||||||||
| \(\ds \) | \(=\) | \(\ds 2 \sin 50 \degrees \cos 10 \degrees\) | Cosine Function is Even |
$\blacksquare$
Sources
- 1953: L. Harwood Clarke: A Note Book in Pure Mathematics ... (previous) ... (next): $\text V$. Trigonometry: Exercises $\text {XXXII}$: $1$.