Question

1.Cos105Cos75
2.2Cos7 30'cos37 303.Sin82 30'cos37 30'найдите значение выражения

Answer 1

$1);cos105^ocos75^o=frac{1}{2}(cos(105^o+75^o)+cos(105^o-75^o))=\frac{1}{2}(cos180^o+cos30^o)=frac{1}{2}(-1+frac{sqrt3}{2})=frac{sqrt3}{4}-frac{1}{2};\\ 2);2cos7^o30'cos37^o30'=\ frac{1}{2}*2(cos(7^o30'+37^o30')+cos(7^o30'-37^o30'))\=cos45^o+cos30^o=frac{sqrt2}{2}+frac{sqrt3}{2}=frac{sqrt2+sqrt3}{2};\\3)sin82^o30'cos37^o 30'=\ frac{1}{2}(sin(82^o30'+37^o30')+sin(82^o30'-37^o30'))=\frac{1}{2}(sin120^o+sin45^o)=frac{1}{2}(frac{sqrt3}{2}+frac{sqrt2}{2})=frac{sqrt3+sqrt2}{4}$