Question

найдите значение выражения:
sin(a-b),если sina*cosb=1/4; a+b=9Π/2

sin(a+b), если sina*cosb=-1/4; a-b=-П/2

Answer 1

$1)Sin(\alpha+\beta)=Sin\frac{9\pi }{2}=Sin(4\pi+\frac{\pi }{2})=Sin\frac{\pi }{2}=1\\\\\underbrace{Sin(\alpha +\beta)}_{1}=\underbrace{Sin\alpha Cos\beta}_{\frac{1}{4}} +Cos\alpha Sin\beta\\\\Cos\alpha Sin\beta= 1-\frac{1}{4}=\frac{3}{4} \\\\Sin(\alpha -\beta)=Sin\alpha Cos\beta-Cos\alpha Sin\beta=\frac{1}{4}-\frac{3}{4}=\boxed{-0,5}$

$2)Sin(\alpha-\beta)=Sin(-\frac{\pi }{2})=-Sin\frac{\pi }{2}=-1\\\\\underbrace{Sin(\alpha -\beta)}_{-1}=\underbrace{Sin\alpha Cos\beta}_{-\frac{1}{4}} -Cos\alpha Sin\beta\\\\Cos\alpha Sin\beta= 1-\frac{1}{4}=\frac{3}{4} \\\\Sin(\alpha +\beta)=Sin\alpha Cos\beta+Cos\alpha Sin\beta=-\frac{1}{4}+\frac{3}{4}=\boxed{0,5}$