Question

Найти cos(a+b), если sina=0.6 и tgb=0,8

Answer 1

$cosa*cosb-sina*sinb\ tgb=frac{sinb}{cosb}=0.8\ frac{sinb}{sqrt{1-sin^2b}}=0.8\ frac{sin^2b}{1-sin^2b}=0.8^2\ sin^2b=0.8^2-0.8^2*sin^2b\ 1.64sin^2b=0.8^2\ sin^2b=frac{0.64}{1.64}\ sinb=+/-frac{0.8}{sqrt{1.64}}\ cosb=sqrt{1-frac{0.8^2}{1.64}}=frac{1}{sqrt{1.64}}\ cosa=sqrt{1-0.6^2}=0.8\ cos(a+b)=0.8*0.6-frac{0.8}{1.64}=0.48-frac{1}{2.05}=-frac{0.016}{2.05}$