Question

sin20*cos10+cos160*cos100/sin21*cos9+cos159*cos99

Answer 1

$dfrac{sin20^circcos10^circ+cos(180^circ-20^circ)cos(90^circ+10^circ)}{sin21^circcos9^circ+cos(180^circ-21^circ)cos(90^circ+9^circ)}=\ \ \ dfrac{sin20^circcos10^circ+(-cos20^circ)cdot(-sin10^circ)}{sin21^circcos9^circ+(-cos21^circ)cdot(-sin9^circ)}=dfrac{sin20^circcos10^circ+cos20^circsin10^circ}{sin21^circcos9^circ+cos21^circsin9^circ}=\ \ =dfrac{sin(20^circ+10^circ)}{sin(21^circ+9^circ)}=dfrac{sin30^circ}{sin30^circ}=1$