Question

Даю 40 баллов! Помогите пожалуйста ​

Answer 1

$1); ; ; ; 2sintcdot sin2t+cos3t=2cdot frac{1}{2}, (cost-cos3t)+cos3t=cost\\\2); ; a); ; cos14^circ cdot cos16^circ =frac{1}{2}, (cos30^circ +cos2^circ )=frac{1}{2}cdot (frac{sqrt3}{2}+cos2^circ )=frac{sqrt3}{4}+frac{cos2^circ }{2}$

$b); ; sin^210^circ +cos50^circ cdot cos70^circ =sin^210^circ +frac{1}{2}, (cos120^circ +cos20^circ )=\\=frac{1-cos20^circ }{2}+frac{1}{2}, (-cos, 60^circ +cos20^circ)=frac{1}{2}-frac{1}{2}, cos20^circ -frac{1}{2}cdot frac{1}{2}+frac{1}{2}, cos20^circ =frac{1}{4}$

$c); ; 3, cosfrac{3pi }{4}cdot cosfrac{5pi }{12}=frac{3}{2}, (cosfrac{7pi}{6}+cosfrac{pi}{3})=frac{3}{2}cdot (cos(pi +frac{pi}{6})+frac{1}{2})=\\=frac{3}{2}cdot (-cosfrac{pi}{6}+frac{1}{2})=frac{3}{2}cdot (frac{1}{2}-frac{sqrt3}{2})$

$3); ; sinacdot cosbeta =frac{1}{4}; ; ,; ; alpha +beta =-frac{pi}{6}\\sinalpha cdot cosbeta =frac{1}{2}, (sin(alpha +beta )+sin(alpha -beta ))\\frac{1}{4}=frac{1}{2}, (sin(-frac{pi}{6})+sin(alpha -beta ))\\frac{2}{4}=-frac{1}{2}+sin(alpha -beta )\\sin(alpha -beta )=1$