Question

sina+cosa=2/3, чему равен sin2a?

Answer 1

$sin alpha +cos alpha = dfrac{2}{3} \\(sin alpha +cos alpha)^2= dfrac{4}{9} \\sin^2 alpha +2sin alpha cos alpha +cos^2 alpha = dfrac{4}{9} \\ 2sin alpha cos alpha= dfrac{4}{9} - 1\\2sin alpha cos alpha= -dfrac{5}{9} \\sin2 alpha =- dfrac{5}{9}$