Sine of 75 Degrees/Proof 2
Jump to navigation
Jump to search
Theorem
- $\sin 75 \degrees = \sin \dfrac {5 \pi} {12} = \dfrac {\sqrt 6 + \sqrt 2} 4$
Proof
| \(\ds \sin 75 \degrees\) | \(=\) | \(\ds \map \cos {90 \degrees - 75 \degrees}\) | Cosine of Complement equals Sine | |||||||||||
| \(\ds \) | \(=\) | \(\ds \cos 15^\circ\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds \frac {\sqrt 6 + \sqrt 2} 4\) | Cosine of $15 \degrees$ |
$\blacksquare$