Упростите [latex] \frac{ \sqrt{2}cosa-2cos(45°-a) }{2sin(30°+a)- \sqrt{3}sina } [/latex]

[latex] \frac{ \sqrt{2}cosa-2(cos45cosa+sin45sina) }{2(sin30cosa+cos30sina)- \sqrt{3}sina }= \\ = \frac{\ \sqrt{2}cosa-2( \frac{ \sqrt{2} }{2}cosa+ \frac{ \sqrt{2} }{2}sina)}{2( \frac{1}{2}cosa+ \frac{ \sqrt{3} }{2}sina)- \sqrt{3}sina }= \\ = \frac{ \sqrt{2}cosa-\sqrt{2}cosa-\sqrt{2}sina }{cosa+ \sqrt{3}sina- \sqrt{3}sina }= \\ = \frac{-\sqrt{2}sina}{cosa}=-\sqrt{2}tga [/latex]