Корни уравнения

Ответ: 216⁰. sin5x = 0 => x = 36⁰, 72⁰. cos3x = cos(90⁰-2x) => 3x = 90⁰ - 2x + 360⁰n U 3x = 2x - 90⁰ +360⁰m => x = 18⁰, 90⁰

Решение. Cos7x + Sin8x = Cos3x - Sin2x sin(8x)+sin(2x)=cos(3x)-cos(7x) 2*sin(5x)*cos(3x)=2*sin(5x)*sin(2x) sin(5x)*(cos(3x)-sin(2x))=0 sin(5x)*(4*(cos(x))^3-3*cos(x)-2*sin(x)*cos(x))=0 sin(5x)*cos(x)*(4*(cos(x))^2-3-2*sin(x))=0 sin(5x)*cos(x)*(4*(1-(sin(x))^2-3-2*sin(x))=0 sin(5x)*cos(x)*(4*(sin(x))^2+2*sin(x)-1)=0 sin(5x)=0 x=пк/5 xЄZ cos(x)=0 x=п/2+пm mЄZ 4*(sin(x))^2+2*sin(x)-1=0 sin(x)=(-1-sqrt(5))/4 x=(-1)^s*arcsin((-1-sqrt(5))/4)+пs sЄZ sin(x)=(sqrt(5)-1)/4 x=(-1)^p*arcsin((sqrt(5)-1)/4) +пp pЄZ п/5+2п/5+arcsin((sqrt(5)-1)/4=36+72+18=126 Проверь.