sin2x= 2*sinx*cosx
<span>(cos(x)-sin(x))^2 = cox^2x -2*sinx*cosx+ sin^2x = -2*sinx*cosx+1</span>
<span> 2*sinx*cosx= - 2*sinx*cosx+1</span>
<span> 4*sinx*cosx = 1 </span>
<span>sinx*cosx = 1/4</span>
<span>(sin2x+sin0)/2 = 1/4</span>
<span>sin2x+sin0 = 0.5</span>
<span>sin 2x = 0.5</span>
<span>2x = (-1)в степени n*П/6+Пn</span>
<span>x = (-1)в степени n*П/12+Пn/2</span>
n = 0 x = П/12
n = 1 x = -П/12+П/2 = 5П/12
n = -1 x = -П/12-Пn/2 = не удовл. условию
n = 2 x = П/12+П = 7П/12
n= 3 х= -П/12+3П/2 = 17П/12
n= 4 n = 2 x = П/12+2П = не удовлетворяет условию
ответ : 3 корня