Question

помогите решить эти два задания

Answer 1

$Cosalpha =-sqrt{1-Sin^{2} alpha}=- sqrt{1-(-frac{15}{17}) ^{2}}= -sqrt{1-frac{225}{289} }=- sqrt{frac{64}{289}}=- frac{8}{17}\\Sinbeta=- sqrt{1-Cos^{2} beta} =- sqrt{1-(frac{8}{17})^{2}}=- sqrt{1-frac{64}{289}}=- sqrt{frac{225}{289}}=- frac{15}{17} \\Cos(alpha+ beta)=Cos alpha Cos beta-Sin alpha Sin beta=- frac{8}{17}* frac{8}{17}-(- frac{15}{17})*(- frac{15}{17})=- frac{64}{289}- frac{225}{289}=- frac{289}{289}=-1$

$2)Sinalpha= sqrt{1-Cos^{2} alpha} = sqrt{1-(frac{3}{5})^{2}}= sqrt{1-frac{9}{25}}=sqrt{frac{16}{25}}= frac{4}{5}\\Sin2alpha =2Sinalpha Cos alpha = 2*frac{4}{5} *frac{3}{5}= frac{24}{25} =0,96\Cos2alpha=2Cos ^{2} alpha -1=2*(frac{3}{5}) ^{2}-1=2* frac{9}{25}-1= frac{18}{25}-1=- frac{7}{25}$

$tg2alpha =frac{Sin2alpha} {Cos2alpha}=  frac{24}{25}:(- frac{7}{25})=- frac{24*25}{25*7}=- frac{24}{7}=-3 frac{3}{7}$