Question

0.5sin20-cos10 /sin3sin17- cos3cos17=√3/2.

Answer 1

$\boldsymbol{\dfrac{0,5~\sin20^o-\cos10^o}{\sin3^o~\sin17^o-\cos3^o~\cos17^o}=}\\ \\ \\ =\dfrac{0,5~\sin20^o-\cos(30^o-20^o)}{-(\cos3^o~\cos17^o-\sin3^o~\sin17^o)}=\\ \\ \\ =\dfrac{0,5~\sin20^o-(\cos30^o~\cos20^o+\sin30^o~\sin20^o)}{-\cos(3^o+17^o)}=\\ \\ \\ =\dfrac{\frac{1}{2}~\sin20^o-\frac{\sqrt{3}}{2}~\cos20^o-\frac{1}{2}~\sin20^o}{-\cos20^o}=\\ \\ \\ =\dfrac{-\frac{\sqrt{3}}{2}~\cos20^o}{-\cos20^o}=\boldsymbol{\dfrac{\sqrt{3}}{2}}$