Question

sin п/12+ cos п/12
вычислите

Answer 1

$sinfrac{pi }{12}+cosfrac{pi }{12}=sqrt2cdot (frac{1}{sqrt2}cdot sinfrac{pi }{12}+frac{1}{sqrt2}cdot cosfrac{pi }{12})=Big [frac{1}{sqrt2}=frac{sqrt2}{2}=cosfrac{pi}{4}=sinfrac{pi}{4}Big ]=\\=sqrt2cdot (cosfrac{pi }{4}cdot sinfrac{pi }{12}+sinfrac{pi }{4}cdot cosfrac{pi }{12})=sqrt2cdot sin(frac{pi}{4}+frac{pi}{12})=\\=sqrt2cdot sinfrac{4pi }{12}=sqrt2cdot sinfrac{pi}{3}=sqrt2cdot frac{sqrt3}{2}=frac{sqrt6}{2}; ; Big (=sqrt{frac{3}{2}}, Big )$

$star ; ; sinalpha cdot cosbeta +sinbeta cdot cosalpha =sin(alpha +beta ); ; star$