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stetique
@stetique
July 2022
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sin3x-2sin2x+sinx+cosx-1=0
умоляю, спасите мою душу
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Vas61
(sin3x+sinx)-2sin2x+cosx-1=0
2sin(3x+x)/2cos(3x-x)/2-2sin2x+cosx-1=0
2sin2xcosx-2sin2x+cosx-1=0
(2sin2xcosx-2sin2x)+(cosx-1)=0
2sin2x(cosx-1)+(cosx-1)=0
(cosx-1)(2sin2x+1)=0
cosx-1=0 или 2sin2x+1=0
cosx=1 2sin2x=-1
x=2πk, k∈Z sin2x=-1/2
2x=(-1)ⁿarcsin(-1/2)+πn arcsin(-1/2)=-arcsin1/2=-π/6
2x=(-1)ⁿ⁺¹π/6+πn
x=(-1)ⁿ⁺¹π/12+πn/2, n∈Z
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Answers & Comments
2sin(3x+x)/2cos(3x-x)/2-2sin2x+cosx-1=0
2sin2xcosx-2sin2x+cosx-1=0
(2sin2xcosx-2sin2x)+(cosx-1)=0
2sin2x(cosx-1)+(cosx-1)=0
(cosx-1)(2sin2x+1)=0
cosx-1=0 или 2sin2x+1=0
cosx=1 2sin2x=-1
x=2πk, k∈Z sin2x=-1/2
2x=(-1)ⁿarcsin(-1/2)+πn arcsin(-1/2)=-arcsin1/2=-π/6
2x=(-1)ⁿ⁺¹π/6+πn
x=(-1)ⁿ⁺¹π/12+πn/2, n∈Z