Question

Найдите sin2a Если sina-cosa=-0.4

Answer 1

$\displaystyle\bf\\Sin\alpha -Cos\alpha =-0,4\\\\(Sin\alpha -Cos\alpha)^{2} =(-0,4)^{2} \\\\Sin^{2}\alpha -2Sin\alpha Cos\alpha +Cos^{2} \alpha =0,16\\\\\underbrace{Sin^{2}\alpha +Cos^{2} \alpha }_{1} -\underbrace{2Sin\alpha Cos\alpha}_{Sin2\alpha } =0,16\\\\1-Sin2\alpha =0,16\\\\Sin2\alpha =1-0,16\\\\\boxed{Sin2\alpha =0,84}$