Tan 150 + cos 60 per tan 150 - cos 60

[tex] \tan(150) + \frac{ \cos(60) }{ \tan(150) } - \cos(60) \\ = - \tan(30) + \frac{ \cos(60) }{ - \tan(30) } - \cos(60) \\ = - \frac{1}{3} \sqrt{ 3} + \frac{ \frac{1}{2} }{ - \frac{1}{3} \sqrt{3} } - \frac{1}{2} \\ = - \frac{ \sqrt{3} }{3} + ( \frac{1}{2} \times - \frac{3}{ \sqrt{3} } ) - \frac{1}{2} \\ = - \frac{ \sqrt{3} }{3} + ( - \frac{ \sqrt{3} }{2} ) - \frac{1}{2} \\ = - \frac{ \sqrt{3} }{3} - \frac{( \sqrt{3 } + 1) }{2} \\ = - (\frac{2 \sqrt{3} + 3 \sqrt{3} + 2 }{6}) \\ = - \frac{5 \sqrt{3} + 3 }{6} [/tex]