Question

Тригонометрические функции

Answer 1

$sinalpha=sqrt{1-cos^2alpha}=sqrt{1-frac{225}{289}}=sqrt{frac{64}{289}}=pmfrac8{17}\frac{3pi}2 textless alpha textless 2piRightarrowsinalpha textless 0\sinalpha=-frac8{17}\\cos2alpha=cos^2alpha-sin^2alpha=frac{225}{289}-frac{64}{289}=frac{161}{289}\\cos(alpha-fracpi6)=cosalphacosfracpi6+sinalphasinfracpi6=frac{15}{17}cdotfrac{sqrt3}2+frac8{17}cdotfrac12=frac{15sqrt3+8}{34}$