Question

Помогите пожалуйста упростить выражения) )

Answer 1

$frac{sinalpha}{2cosfrac{alpha}{2} } =frac{2sinfrac{alpha}{2}cosfrac{alpha}{2}}{2cosfrac{alpha}{2} } =sinfrac{alpha}{2}$

$frac{cosalpha}{sinfrac{alpha}{2}-cosfrac{alpha}{2}}=frac{cos^2frac{alpha}{2}-sin^2frac{alpha}{2}}{sinfrac{alpha}{2}-cosfrac{alpha}{2}}=frac{(cosfrac{alpha}{2}-sinfrac{alpha}{2})(cosfrac{alpha}{2}+sinfrac{alpha}{2})}{sinfrac{alpha}{2}-cosfrac{alpha}{2}}=-sinfrac{alpha}{2}-cosfrac{alpha}{2}$

$1-2sin^2(45+1.5alpha)=1-2cdot frac{1-cos(90+3alpha)}{2}=1-1+cos(90+3alpha)=cos(90+3alpha)=-sin3alpha$

$sinfrac{alpha}{2}cosfrac{alpha}{2}cosalpha=frac{2sinfrac{alpha}{2}cosfrac{alpha}{2}cosalpha}{2}=frac{sinalpha cosalpha}{2}=frac{2sinalpha cosalpha}{4}=frac{sin2alpha}{4}$