[tex]\displaystyle\bf\\\Big(sin\propto+cos\propto\Big)^2=\\\\=sin^2\propto+2sin\propto cos\propto+cos^2\propto=\\\\=\underbrace{sin^2\propto+cos^2\propto}_{=1}+\underbrace{2sin\propto cos\propto}_{=sin2\propto}=\\\\\\=\boxed{\bf1+sin\,2\!\propto}[/tex]