Question

На до доказать тождество
Sin(45-альфа)/cos(45+альфа)=1

Answer 1

$sin( alpha - beta )=sin alpha cos beta -cos alpha sin beta \ cos( alpha + beta )=cos alpha cos beta -sin alpha sin beta \ \ frac{sin(45- alpha )}{cos(45+ alpha )} = frac{sin45cos alpha -cos45sin alpha }{cos45cos alpha -sin45sin alpha } = frac{ frac{ sqrt{2} }{2}cos alpha - frac{ sqrt{2} }{2}sinalpha}{frac{ sqrt{2} }{2}cos alpha-frac{ sqrt{2} }{2}sinalpha} =1$