Question

вычислить sin75+sin45/sin285

Answer 1

sin(75°)+sin(45°)/sin(285°)=sin(30°+45°)+sin(45°)/(sin(180°+(60°+45°))=
=sin(30°)cos(45°)+cos(30°)sin45°)+sin(45°)/(-sin(60°+45°))=
=(1/2)*(1/sqrt(2))+(sqrt(3))*(1/sqrt(2))+(1/sqrt(2))/(-(sin(60°)cos(45°)+cos(60°)*sin(45°)))=(1+sqrt(3))/2sqrt(2))+(1/sqrt(2))/(-(sqrt(3)/2)(1/sqrt(2))+(1/2)(1/sqrt(2))=
(1+sqrt(3))/2sqrt(2))+(1/sqrt(2))/(-(1/sqrt(2))((1+sqrt(3))/2))
=(1/2sqrt(3))/2sqrt(3))-2sqrt(2))/(1+sqrt(3))=(sqrt(3)-2)/(sqrt(2)+sqrt(6))