Question

tg a=3 значение  выражения sin2a-cos2a равно

Answer 1

$tg^2 alpha +1 =frac{1}{cos^2 alpha }\ \ tg alpha=frac{sin alpha}{cos alpha}=3; sin alpha=3cos alpha \ \ sin 2alpha-cos2alpha=2sin alpha cos alpha - cos^2 alpha+ sin^2 alpha =\\=2 cdot 3cos alpha cos alpha -cos^2 alpha +9cos^2 alpha =6cos^2 alpha+8 cos^2 alpha=14cos^2 alpha=\\=14 cdot (frac{1}{tg^2 alpha +1})=frac{14}{3^3+1}=frac{14}{10}=frac{7}{5}$