Question

Найдите значение выражения: 4sin^2(75°)

Answer 1

$4sin^2(75^{\circ})\\sin(75^{\circ})=sin(30^{\circ}+45^{\circ})\\sin(30^{\circ})cos(45^{\circ})+cos(30^{\circ})sin(45^{\circ})\\\frac{1}{2}\cdot \frac{\sqrt{2}}{2}+\frac{\sqrt{3}}{2}\cdot \frac{\sqrt{2}}{2}=\frac{\sqrt{2}+\sqrt{6}}{4}\\\\4sin^2(75^{\circ})=\frac{2+4\sqrt{3}+6}{4}=2+\sqrt{3}$