Question

Aratati ca sin π/12= \frac{ \sqrt{6} - \sqrt{2} }{ 4}

Answer 1

Salut,

$\sin\dfrac{\pi}{12}=\sin\left(\dfrac{4\pi-3\pi}{12}\right)=\sin\left(\dfrac{\pi}{3}-\dfrac{\pi}{4}\right)=\sin\dfrac{\pi}{3}\cdot\cos\dfrac{\pi}{4}-\cos\dfrac{\pi}{3}\cdot\sin\dfrac{\pi}{4}=\\\\=\dfrac{\sqrt3}2\cdot\dfrac{\sqrt2}2-\dfrac{1}2\cdot\dfrac{\sqrt2}2=\dfrac{\sqrt6-\sqrt2}4,\ ceea\ ce\ trebuia\ demonstrat.\ A\ fost\ greu\ ?$

Green eyes.

Answer 2

π/12 = 180°/12 = 15°

[tex]\it sin15^o = sin(45^o-30^o) = sin45^ocos30^o-sin30^ocos45^o= \\\;\\ \\\;\\ = \dfrac{\sqrt2}{2}\cdot\dfrac{\sqrt3}{2} -\dfrac{1}{2} \cdot\dfrac{\sqrt2}{2} =\dfrac{\sqrt6-\sqrt2}{4}[/tex]