Question

Преобразуйте в произведение:
1) cos 7x - cos 17x
2) Корень 11 sin 3a + 2cos 3a

Answer 1

$1); ; cos7x-cos17x=-2cdot sinfrac{7x-17x}{2}cdot sinfrac{7x+17x}{2}=2cdot sin5xcdot sin12x\\2)quad sqrt{11}sin3a+2cos3a=[; (sqrt{11})^2+2^2=11+4=15; ]=\\=sqrt{15}cdot left (frac{sqrt{11}}{sqrt{15}}cdot sin3a+frac{2}{sqrt{15}}cdot cos3aright )=\\=Big [; tak; kak; left (frac{sqrt{11}}{sqrt{15}}right )^2+left (frac{2}{sqrt{15}}right )^2=1,; to ; frac{sqrt{11}}{sqrt{15}}=cos beta ,; frac{2}{sqrt{15}}=sinbeta ; Big ]=\\=sqrt{15}cdot Big (cos beta cdot sin3a+sin beta cdot cos3aBig )=sqrt{15}cdot sin(3a+ beta ),; ; tgbeta =frac{2}{sqrt{11}}$