Question

75cos(2 arccos 4/5) найдите значение выражения

Answer 1

$75cdot cos(2cdot arccosfrac{4}{5})=75cdot (cos^2(arccosfrac{4}{5})-sin^2(arccosfrac{4}{5}))=\\=75cdot ((frac{4}{5})^2-(frac{3}{5})^2)=75cdot frac{16-9}{25}=3cdot 7=21\\\sin(arccosfrac{4}{5})=sin alpha ,; alpha =arccosfrac{4}{5}; to ; cos alpha =frac{4}{5}\\sin^2 alpha =1-cos^2 alpha =1-(frac{4}{5})^2=frac{3}{5}$