6sinx+5cosx=6 необходимо решение

   Воспользуемся формулами двойных углов синуса и косинуса:

• sin(2) = 2sin * cos;
• cos(2) = cos^2() - sin^2();

• 6sinx + 5cosx = 6;
• 5cosx - 6(1 - sinx) = 0;
• 5(cos^2(x/2) - sin^2(x/2)) - 6(cos^2(x/2) - 2cos(x/2)sin(x/2) + sin^2(x/2)) = 0;
• 5(cos(x/2) - sin(x/2))(cos(x/2) + sin(x/2)) - 6(cos(x/2) - sin(x/2))^2 = 0;
• (cos(x/2) - sin(x/2))(5cos(x/2) + 5sin(x/2) - 6cos(x/2) + 6sin(x/2)) = 0;
• (cos(x/2) - sin(x/2))(11sin(x/2) - cos(x/2)) = 0;

• [cos(x/2) - sin(x/2) = 0;
  [11sin(x/2) - cos(x/2) = 0;
• [sin(x/2) = cos(x/2);
  [11sin(x/2) = cos(x/2);
• [tg(x/2) = 1;
  [tg(x/2) = 1/11;
• [x/2 = /4 + k, k Z;
  [x/2 = arctg(1/11) + k, k Z.
• [x = /2 + 2k, k Z;
  [x = 2arctg(1/11) + 2k, k Z.

   Ответ: /2 + 2k; 2arctg(1/11) + 2k, k Z.