Решить уравнение cos x - корень из 3sin x=2cos 7x, записать число корней на промежутке [0 градусов и 180]

2 (1/2cosx-√3/2sinx) = 2cos7x

2cos (x+π/3) = 2cos7x

cos7x-cos (x+π/3) = 0

-2sin (4x+π/6) sin (3x-π/6) = 0

sin (4x+π/6) = 0⇒4x+π/6=πn⇒4x=-π/6+πn⇒x=-π/24+πn/4

0≤-π/24+πn/4≤π

0≤-1+6n≤24

1≤6n≤25

1/6≤n≤25/9

n=1⇒x=-π/24+π/4=5π/24

n=2⇒x=-π/24+π/2=11π/24

n=3⇒x=-π/24+3π/4=17π/24

n=4⇒x=-π/24+π=23/π/24

sin (3x-π/6) = 0⇒3x-π/6=πn⇒3x=π/6+πn⇒x=π/18+πn/3

0≤π/18+πn/3≤π

0≤1+18n≤18

-1≤18n≤17

-1/18≤n≤17/18

n=0⇒x=π/18