1)вычислить Sin(p/48)*cos(p/48)*cos(p/24)*cos(p/12) 2)решите уравнение 26 sinx * cos x -cos4x+7=0 3)sin^2(2x-p/6)=3/4

   1)

• A = sin(/48) * cos(/48) * cos(/24) * cos(/12);
• A = 1/2sin(/24) * cos(/24) * cos(/12);
• A = 1/4sin(/12) * cos(/12);
• A = 1/8sin(/6) = 1/8 * 1/2 = 1/16.

   2)

• 26sinx * cosx - cos4x + 7 = 0;
• 13sin2x - (1 - 2sin^2(2x)) + 7 = 0;
• 2sin^2(2x) + 13sin2x + 6 = 0;
• D = 13^2 - 4 * 2 * 6 = 169 - 48 = 121;
• sin2x = (-13 121)/4 = (-13 11)/4;
• 1) sin2x = (-13 - 11)/4 = -24/4 = -6 lt; -1 - нет решений;
• 2) sin2x = (-13 + 11)/4 = -2/4 = -1/2;
• 2x = -/2 /3 + 2k, k Z;
• x = -/4 /6 + k, k Z.

   3)

• sin^2(2x - /6) = 3/4;
• sin(2x - /6) = 3/2;
• 2x - /6 = /3 + k, k Z;
• 2x = /6 /3 + k, k Z;
• x = /12 /6 + k/2, k Z.

   4)

• sin^2(x/2) = cos^2(7x/2);
• 2cos^2(7x/2) - 2sin^2(x/2) = 0;
• (2cos^2(7x/2) - 1) + (1 - 2sin^2(x/2)) = 0;
• cos7x + cosx = 0;
• 2cos4x * cos3x = 0;

• [cos4x = 0;
  [cos3x = 0;
• [4x = /2 + k, k Z;
  [3x = /2 + k, k Z;
• [x = /8 + k/4, k Z;
  [x = /6 + k/3, k Z.