Question

курс 3 подробно срочно пожалуйста

Answer 1

$frac{cos(2pi - alpha )+sin(pi - alpha )}{cos(2pi + alpha )+sin(pi + alpha )} -frac{cos( alpha +sin(- alpha )}{cos(2pi - alpha )+sin(pi - alpha )} =\\= frac{cos alpha +sin alpha }{cos alpha -sin alpha } -frac{cos alpha -sin alpha }{cos alpha +sin alpha } = frac{(cos alpha +sin alpha )^2-(cos alpha -sin alpha )^2}{cos^2 alpha -sin^2 alpha } =$

 $= frac{1+2sin alpha cdot cos alpha -(1-2sin alpha cdot cos alpha )}{cos2 alpha } = frac{2cdot sin2alpha }{cos2 alpha }$ $=2tg alpha$  

$alpha =15^circquad Rightarrow ; ; ; 2tg(2cdot 15^circ )=2tg30^circ =frac{2sqrt3}{3}$