Sine of 75 Degrees/Proof 2

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 $15 \degrees$

$\blacksquare$

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