Question

Вычислите: sin(2arksin1/3)?

Answer 1

$sin(2arcsin\frac{1}{3})=2\cdot sin(arcsin\frac{1}{3})\cdot cos(arcsin\frac{1}{3})=\\\\=2\cdot \frac{1}{3}\cdot \sqrt{1-sin^2(arcsin\frac{1}{3})}=\frac{2}{3}\cdot \sqrt{1-(\frac{1}{3})^2}=\frac{2}{3}\cdot \sqrt{1-\frac{1}{9} }=\\\\=\frac{2}{3}\cdot \sqrt{\frac{8}{9}}=\frac{2\cdot 2\sqrt2}{3\cdot 3}=\frac{4\sqrt2}{9}$