Question

Sin(pi/4 - α) , если sinα= √2/3 и pi/2

Answer 1

$cos \alpha =- \sqrt{1- \frac{2}{9} }=- \frac{ \sqrt{7} }{3} \\sin( \frac{ \pi }{4} - \alpha )=sin\frac{ \pi }{4}cos \alpha -sin \alpha cos\frac{ \pi }{4}= \frac{ \sqrt{2} }{2} (cos \alpha -sin \alpha )=\\= -\frac{ \sqrt{2} }{6} (\sqrt{7} + \sqrt{2} )$