1/2sin(6x-2x)+1/2sin(6x+2x)<1/2sin(5x-3x)+1/2sin(5x+3x)
1/2sin4x+1/2sin8x<1/2sin2x+1/2sin8x
1/2sin4x-1/2sin2x<0
1/2*2sin2xcos2x-1/2sin2x<0
1/2sin2x(2cos2x-1)<0
1){sin2x>0⇒2πk<2x<π+2πk⇒πk<x<π/2+πk,k∈z
{cos2x<1/2⇒π/3+2πk<2x<5π/3+2πk⇒π/6+πk<x<5π/6+πk,k∈z
x∈(π/6+πk;π/2+πk,k)
2){sin2x<0⇒π+2πk<2x<2π+2πk⇒π/2+πk<x<π+πk,k∈z
{cos2x>1/2⇒-π/3+2πk<2x<π/3+2πk⇒-π/6+πk<x<π/6+πk,k∈z
x∈(-π/6+πk;πk,k∈Z)
Ответ x∈(-π/6+πk;πk,k∈Z) U (π/6+πk;π/2+πk,k)
25*2=50
50-25=25 вот и все)
1. х+5=4х-7 ⇒ 3х=12 ⇒ х=4 ОДЗ: х+5>0 и 4х-7>0
Ответ: х=4
2. sin x = t -1≤t≤1
3t^2-7t+4=0 D = 49-48=1 t=(7+1)/6=4/3 t=(7-1)/6=1
4/3 не подходит.
sin x=1 ⇒ x=π/2+2πn, где n∈Z
3. производная функции f(x)= 13x^12-22x^10+40x^7+2x-1