Question

Упростить выражение:
$\frac{ \sqrt{3}cos2 \alpha + sin2 \alpha}{cos \alpha +\sqrt{3}sin\alpha}$

Answer 1

2(√3/2*cos2a+1/2*sin2a)/2(1/2*cosa+√3/2*sina)=sin(2a+π/3)/sin(a+π/6)=
=2sin(a+π/6)cos(a+π/6)/sin(a+π/6)=2cos(a+π/6)

Answer 2

$\frac{ \sqrt{3}cos 2a+sin2a }{cosa+ \sqrt{3}sina }$ = $\frac{-(2 \sqrt{3} sin^2a-2cosa sina- \sqrt{3} }{ \sqrt{3}sina+cosa}$ = $\frac{2cosa sina+2 \sqrt{3}cos^2a- \sqrt{3} }{ \sqrt{3} sina+cosa}$ = $\sqrt{3} cosa-sina$