sin 3/4 π + tan π + cos π / sin 1/2 π + cos 2π - 3 cos 1/3π

[tex] \frac{ \sin( \frac{3}{4}\pi ) + \tan(\pi) + \cos(\pi) }{ \sin( \frac{1}{2} \pi) + \cos(2\pi) - 3 \cos( \frac{1}{3} \pi) } \\ = \frac{ \sin( \frac{3}{4}(180) ) + \tan(180) + \cos(180) }{ \sin( \frac{180}{2} ) + \cos(2(180)) - 3 \cos( \frac{180}{3} ) } \\ = \frac{ \sin(135) + \tan(180) + \cos(180) }{ \sin(90) + \cos(360) - 3 \cos(60) } \\ = \frac{ \frac{ \sqrt{2} }{2} + 0 - 1 }{1 + 1 - \frac{3}{2} } \\ = \frac{ \sqrt{2} + 0 - 2 }{2} \div \frac{2 + 2 - 3}{2} \\ = \frac{ \sqrt{2} - 2}{2} \times \frac{2}{2 + 2 - 3} \\ = \frac{ \sqrt{2} - 2}{2 + 2 - 3} \\ = \frac{ \sqrt{2} - 2}{1} = \sqrt{2} - 2[/tex]