Task/24844413
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а)
sin10x -cos4x =0 ;
sin10x - sin(π/2 - 4x) =0 ; * * * sinα -sinβ =2sin(α-β)/2 * cos(α+β)/2 * * *
2sin(7x -π/4)*cos(3x +π/4) =0 ;
а₁)
sin(7x -π/4) =0
7x -π/4 =πn , n∈Z ;
x = π/28 +πn/7 , n ∈ Z .
a₂)
cos(3x +π/4) =0 ;
3x +π/4 =π/2 + πn , n∈Z ;
x =π/12 + πn/3 , n∈Z .
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б)
sin7x -cos13x =0 ;
sin7x - sin(π/2 -13x) =0 ;
2sin(10x -π/4)*cos(3x -π/4) =0 ;
* * * cos(7x+π/2 -13x)/2 =cos-(3x-π/4) = cos(3x-π/4) * * *
sin(10x -π/4) = 0 или cos(3x -π/4) =0 ;
10x -π/4 = πn или 3x -π/4 = π/2 + πn
x = π/40 + πn/10 или x =π/4 + πn/3 , n∈Z.
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в)
tg5x -ctg3x=0 ;
* * * tgα -ctgβ =sinα/cosα -cosβ/sinβ =(sinαsinβ -cosαcosβ)cosαsinβ =
-cos(α+β) /cosαsinβ * * *
- cos8x / cos5x*sin3x =0 ; * * *ОДЗ: cos5x ≠0 ; sin3x ≠0 * * *
cos8x =0 ;
8x =π/2 +πn , n ∈ Z ;
x = π/16 +πn/8 , n ∈ Z .
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г)
sin10x -cos3x =0 ;
sin10x - sin(π/2 -3x) =0 ;
2sin(13x/2 -π/4)*cos(7x/2 +π/4) =0 ;
г₁)
sin(13x/2 -π/4) =0
13x/2 -π/4=πn , n∈Z ;
x = π/26 +2πn/13 , n∈Z
г₂)
cos(7x/2 +π/4) =0 ;
7x/2 +π/4 =π/2 + πn , n∈Z ;
x =π/14 + 2πn/7 , n∈Z .
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