Question

тригонометрия последние два задания

Answer 1

$10. sqrt3cosalpha-2cos(alpha-pi/6)=sqrt3cosalpha-2(cosalpha*cosfrac{pi}{6}+\+sinalpha*sinfrac{pi}{6})=sqrt3cosalpha-2(frac{sqrt3}{2}cosalpha+frac{1}{2}sinalpha)=\=sqrt3cosalpha-sqrt3cosalpha-sinalpha=-sinalpha$

$11. sinalpha=frac{8}{17}, cosalpha=sqrt{1-sin^2alpha}=sqrt{1-frac{64}{289}}=sqrt{frac{225}{289}}=frac{15}{17}\ cosbeta=frac{4}{5}, sinbeta=sqrt{1-cos^2alpha}=sqrt{1-frac{16}{25}}=frac{3}{5}\ sin(alpha+beta)=sinalpha*cosbeta+cosalpha*sinbeta\ sin(alpha+beta)=frac{8}{17}*frac{4}{5}+frac{15}{17}*frac{3}{5}=frac{77}{85}\ alpha+beta=arcsinfrac{77}{85}$