Question

Спростіть вираз:
cos (900- β) + 2 sin β - 3 cos (900-β)=

Answer 1

Объяснение:

см фото,,,,,,,,,,,,,,,,,,,,,,,,,

Answer 2

$Cos(900^\circ-\beta)+2Sin\beta-3Cos(900^\circ-\beta)=2Sin\beta-2Cos(900^\circ-\beta)=\\\\=2[Sin\beta -Cos(360^\circ\cdot2+(180^\circ-\beta))] =2[Sin\beta-Cos(180^\circ-\beta)] =\\\\=2(Sin\beta +Cos\beta)=2[Sin\beta +Sin(\dfrac{\pi }{2}-\beta)]=2\cdot2Sin\dfrac{\beta+\frac{\pi }{2} -\beta}{2} Cos\dfrac{\beta -\frac{\pi }{2}+\beta}{2}=$

$=4Sin\dfrac{\pi }{4}Cos\Big(\beta-\dfrac{\pi }{4}\Big)=4\cdot\dfrac{\sqrt{2} }{2}\cdot Cos\Big(\beta-\dfrac{\pi }{4}\Big)=\boxed{2\sqrt{2}Cos\Big(\ \beta-\dfrac{\pi }{4}\Big)}$