Question

Sin20*cos10+cos160*cos100/sin21*cos9+cos159*cos99

Answer 1

$\dfrac{\sin20^\circ\cos10^\circ+\cos(180^\circ-20^\circ)\cos(90^\circ+10^\circ)}{\sin21^\circ\cos9^\circ+\cos(180^\circ-21^\circ)\cos(90^\circ+9^\circ)}=\\ \\ \\ \dfrac{\sin20^\circ\cos10^\circ+(-\cos20^\circ)\cdot(-\sin10^\circ)}{\sin21^\circ\cos9^\circ+(-\cos21^\circ)\cdot(-\sin9^\circ)}=\dfrac{\sin20^\circ\cos10^\circ+\cos20^\circ\sin10^\circ}{\sin21^\circ\cos9^\circ+\cos21^\circ\sin9^\circ}=\\ \\ =\dfrac{\sin(20^\circ+10^\circ)}{\sin(21^\circ+9^\circ)}=\dfrac{\sin30^\circ}{\sin30^\circ}=1$