№22) 1 - Sin(x/2 - 3π) - Cos²x/4 + Sin²x/4 =
= 1 + Sin(3π - x/2) - Cos²x/4 + Sin²x/4 =
= Sinx/2 + 2 Sin²x/4= 2Sinx/4Cosx/4 +2Sin²x/4 =
= 2Sinx/4(Cosx/4 + Sinx/4)
№24) 7 + 2Sin2x + 1,5* 1/CosxSinx = 0
7 + 2Sin2x + 1,5 * 2/2SinxCosx = 0
7 + 2Sin2x +3/Sin2x = 0 | *Sin2x ≠0
7Sin2x +2Sin²2x +3 = 0
2Sin²2x +7Sin2x +3 = 0
Решаем как квадратное:
D = b² -4ac = 49 - 4*2*3 = 25
Sin2x = -1/2 Sin2x = -3(нет решений)
2x = (-1)^narcSin(-1/2) + nπ, n ∈Z
2x = (-1)^(n+1) π/6 + nπ, n ∈Z
x = (-1)^(n+1) π/12 + nπ/2, n ∈Z