Sin(6a+a)/sina - 2cos2a-2cos4a-1=(sin6acosa+cos6asina/sina - 2cos6a) - 2cos2a-2cos4a-1=sin6acosa+cos6asina=2cos6asina/sina - 2cos2a-2cos4a-1=sin6acosa-cos6asina/sina - 2cos2a-2cos4a-1=(sin5a/sina - 2cos4a) - 2cos2a-1= ( sin(4a+a)/sina - 2cos4a) - 2cos2a-1=(sin4acosa+cos4asina/sina - 2cos4a) - 2cos2a-1= sin4acosa+cos4asina-2cos4asin/sina - 2cos2a-1=sin4acosa-cos4asina/sina-2cos2a-1=sin3a/sina-2cos2a-1=(sin(2a+a)/sina=2cos2a)-1=(sin2acosa+cos2asina/sina - 2cos2a) -1=sin2acosa+cos2asina-2cos2asina/sina-1=sin2acosa-cosa-cos2asina/sina-1=sina/sina-1=1-1=0.
1. 16х^2-24ху+9у^2-(6x^2-10xy+3xy-5y^2)
16х^2-24ху+9у^2-<span>6x^2+10xy=3xy+5y^2
</span>10x^2+14y^2-17xy
Функция возрастает на промежке, где ее производная больше нуля.
π/6 + x/3 ∈ (-π/2 + 2πn; π/2 + 2πn), n ∈ Z
x/3 ∈ (-2π/3 + 2πn; π/3 + 2πn), n ∈ Z
x ∈ (-2π + 2πn; π + 2πn), n ∈ Z
Функция возрастает при x ∈ (-2π + 2πn; π + 2πn), n ∈ Z.
везде применяем метод интервалов
1.
(x+2)(x-3)(x-4) < 0
------------ (-2) +++++++++ (3) ------------- (4) ++++++++++
x∈(-∞ -2) U (3 4)
2
(x+5)/(x-2)/(x-1)^2 >=0
++++++++++ [-5] ------------ (1) ------------ [2] +++++++++++
x∈(-∞ -5] U [2 +∞)
3
(2x+1)/(x-3) <=1
(2x+1)/(x-3) - 1<=0
(2x+1 - x + 3)/(x-3)<=0
(x+4)/(x-3)<=0
+++++++ [-4] ------------- (3) +++++++
x∈[-4 3)
4
x/(x-4) + 5/(x-1) + 24/(x-1)(x-4) <=0
(x(x-1) + 5(x-4) + 24)/(x-1)(x-4) <=0
(x^2 - x + 5x - 20 + 24) /(x-1)(x-4) <=0
(x^2-4x+4)/(x-1)(x-4) <=0
(x-2)^2/(x-1)(x-4) <=0
++++++++ (1) -----------[2] ---------- (4) ++++++++
x∈(1 4)
/x+y=3
\2x-y=3
/y=3-x
\y=3-2x
x|2|3
y|1|0
x|0|1
y|3|1
потом чертишь график по этим координатам