Question

2sinx*cosx+sqrt{3}-2cosx-sqrt{3}sinx=0

 

Answer 1

$2sinx*cosx + sqrt{3} - 2cosx - sqrt{3}sinx = 0$

$sqrt{3}(1-sinx) - 2cosx(1-sinx) = 0$ 

$(1-sinx)(sqrt{3}-2cosx) = 0$ 

1-sinx = 0   или 2cosx = sqrt(3)

 sinx=1

$x = frac{pi}{2}+2pi n,$ n - целое

$cosx = frac{sqrt{3}}{2}$ 

$x = frac{pi}{6}+2pi n,$ n - целое