cos 140-cos100/sin140-sin100

[tex]
\frac{\cos{140\degree}-\cos{100\degree}}{\sin{140\degree}-\sin{100\degree}}\\
=\frac{-2\sin{\left(\frac{140\degree+100\degree}{2}\right)}\sin{\left(\frac{140\degree-100\degree}{2}\right)}}{2\cos{\left(\frac{140\degree+100\degree}{2}\right)}\sin{\left(\frac{140\degree-100\degree}{2}\right)}}\\
=-\tan{120\degree}\\
=-\tan{(180\degree-60\degree)}\\
=\tan{60\degree}\\
=\sqrt{3}\\
[/tex]