Question

СРОЧНО дано:cosa=1/√6 , -пи/2<α<0 Вычислить: √45⋅sin⁡2 x

Answer 1

$cosa=\dfrac{1}{\sqrt6}\ \ ,\\\\-\dfrac{\pi}{2}<a<0\ \ \ \to \ \ \ sina<0\\\\sin^2a=1-cos^2a=1-\dfrac{1}{6}=\dfrac{5}{6}\ \ ,\ \ sina=-\sqrt{\dfrac{5}{6}}\\\\sin2a=2\, sina\cdot cosa=-2\cdot \sqrt{\dfrac{5}{6}}\cdot \dfrac{1}{\sqrt6}=-\dfrac{2\sqrt5}{6}\\\\\\\sqrt{45}\cdot sin2a=-\dfrac{\sqrt{45}\cdot 2\sqrt5}{6}=-\dfrac{\sqrt{9\cdot 5}\cdot 2\sqrt5}{6}=-\dfrac{3\cdot 5\cdot 2}{6}=-5$