Question

если tg(a/2) = √2, то cos2a = ?...

Answer 1

$tgfrac{a}{2}=sqrt2; ,; ; cos2a=?\\Formylu:; ; ; cos2a=2cos^2a-1; ;; ; ; cosa=frac{1-tg^2frac{a}{2}}{1+tg^2frac{a}{2}}; ;\\cosa=frac{1-(sqrt2)^2}{1+(sqrt2)^2}=frac{1-2}{1+2}=-frac{1}{3}cos2a=2cdot (-frac{1}{3})^2-1=frac{2}{9}-1=-frac{7}{9}$