Question

Вычислите: sin(2arksin1/3)?

Answer 1

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