Вычислить! 25 ! 2cos^2 3x+cos3x+cos9x=1

2cos^2 3x+cos3x+cos9x=1 ⇒2cos²3x+2cos((3x+9x)/2)*cos((3x-9x)/2)=1  ⇒ 2cos²3x+2cos6x*cos3x=1⇒1+cos6x+2cos6x*cos3x=1⇒cos6x(1+2cos3x)=0⇒1случай)cos6x=0⇒6x=π/2+πn⇒x=π/12+πn/6; 2 случай)1+2cos3x=0⇒cos3x=-1/2⇒3x=+-arccos(-1/2)+2πn⇒3x=+-2π/3+2πn⇒x=+-2π/9+2πn/3;

ответ: x=π/12+πn/6; x=+-2π/9+2πn/3;

Sinx + siny = 1/2 sinx * siny = -1/2 sinx = 1/2 - siny (1/2 - siny)*siny = -1/2 sinx = 1/2 - siny 1/2siny - sin²y + 1/2 = 0 siny = t 1/2t - t² + 1/2 = 0 t² - 1/2t - 1/2 = 0 2t² - t - 1 = 0 t = 1 t = -1/2 siny = 1 siny = -1/2 sinx₁ = 1/2 - siny₁ siny₁ = 1 sinx₁ = -1/2 siny₁ = 1 x₁ = -π/6 + 2πn x₂ = -5π/6 + 2πn y₁ =  π/2 + 2πn sinx₃ = 1/2 - siny₂ siny₂ = -1/2 sinx₃ = 1 siny₂ = -1/2 x₃ = π/2 + 2πn y₂ = -π/6 + 2πn y₃ = -5π/6 + 2πn ответ: (π/2 + 2πn;   -π/6 + 2πn); (π/2 + 2πn; -5π/6 + 2πn); (-π/6 + 2πn; π/2 + 2πn); (-5π/6 + 2πn; π/2 + 2πn);   n∈z

A< 2    -->                                       5a< 10 b> 3    >   -b< -3    >   -3b< -9                                                           5a-3b< 10-9                                                         5a-3b< 1