Question

sin^2a+sin^2b+ cos(a+b)*cos(a-b)=a. а-альфа в-бета

Answer 1

$star ; ; cosxcdot cosy=frac{1}{2}(cos(x-y)+cos(x+y)); ; star \\\sin^2 alpha +sin^2 beta +cos( alpha + beta )cdot cos( alpha - beta )=\\=sin^2 alpha +sin^2 beta +frac{1}{2}(cos2 beta +cos2 alpha )=\\=quad star; ; [; cos2x=1-2sin^2x; ]; ; star =\\=sin^2 alpha +sin^2 beta +frac{1}{2}(1-2sin^2 beta +1-2sin^2 alpha )=\\=sin^2 alpha +sin^2 beta +frac{1}{2}-sin^2 beta +frac{1}{2}-sin^2 alpha =1$