\(\frac {sin30° + tan 45° - cosec 45° }{sec30° + cos60° + cot 45°}\)
\(= \cfrac {\frac12 + 1 - \sqrt2}{\frac2{\sqrt 3} + \frac 12 + 1}\)
\(= \cfrac {\frac 32 - \sqrt 2}{\frac 32 + \frac 2{\sqrt3}}\)
\(= \cfrac{\frac{3 - 2\sqrt 2}2}{\frac{3\sqrt 3 + 4} {2\sqrt 3}}\)
\(= \frac {(3 - 2\sqrt 2) (3\sqrt 3 - 4)\sqrt 3}{(3\sqrt 3 + 4)(3\sqrt 3 - 4)}\)
\(= \frac {(9\sqrt 3 - 6\sqrt 6 - 12 + 8\sqrt 2)\sqrt 3}{27 - 16}\)
\(=\frac 1{11} (9\sqrt 3 - 6\sqrt 6 + 8\sqrt2 -12) \sqrt 3\)
