Пусть в 1 цехе изготовили Х деталей. Тогда во 2 изготовили 2х деталей, а в 3 цеху (2х-500) деталей. Составим и решим уравнение
х+2х+2х+500=6000
5х=5500
х=1100
2х=2*1100=2200
2х+500=2200+500=2700
(Х-7)=5
х=7+5
х=13
Проверка:(13-7)=5
5=5
1)sin(α-β)=sinαsinβ-cosαcosb
sin(3π/4-7π/4)=sin(-π)
2)cos(α+β)=cosαcosβ-sinαsinβ
cos(π/7+6π/7)=cosπ=-1
(cos 7x -cos3x) +(sin8x+sin2x) =0;
- 2sin2xsin5x +2sin5xcos3x = 0;
sin5x(sin2x -cos3x) =0 ;
sin5x=0 ⇒ x =π*k/5 ,k ∈Z .
sin2x -cos3x =0
sin2x -sin(π/2 -3x) =0;
2sin(5x/2 -π/4)*cos(π/4 -x/2) =0 ;
sin(5x/2 -π/4)*cos(x/2 -π/4 ) =0 ;
sin(5x/2 -π/4) =0⇒5x/2 -π/4 =π*k ⇔ x = π/10+2π/5*k,k ∈Z
cos(x/2 -π/4)= 0 ⇒x/2 - π/4 =π/2 +π*k ⇔ x=3π/2+2π*k ,k∈Z
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<em>sin2x -cos3x=0;</em>
<em>2sinxcosx -cosx(4cos²x -3) =0;²</em>
<em>cosx(2sinx -4cos²x +3) =0</em>
<em>cosx(4sin²x +2sinx -1) =0</em>