Question

Упростите $frac{ sqrt{2}cosa-2cos(45°-a) }{2sin(30°+a)- sqrt{3}sina }$

Answer 1

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