`~rai~`
\(1.\sin(x-y)\cos y+\cos(x-y)\sin y\\=\sin(x-y+y)\\=\sin x.\\\text{Áp dụng công thức:}\sin(a+b)=\sin a\cos b+\cos a\sin b.\\2.\sin\alpha+\cos\alpha=\dfrac{1}{4}\\\Leftrightarrow (\sin\alpha+\cos\alpha)^2=\left(\dfrac{1}{4}\right)^2\\\Leftrightarrow \sin^2\alpha+2\sin\alpha\cos\alpha+\cos^2\alpha=\dfrac{1}{16}\\\Leftrightarrow 1+2\sin\alpha\cos\alpha=\dfrac{1}{16}\\\Leftrightarrow 2\sin\alpha\cos\alpha=-\dfrac{15}{16}\\\Leftrightarrow \sin\alpha\cos\alpha=-\dfrac{15}{32}.\)