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elvira1234123
@elvira1234123
July 2022
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sinx+sin2x+sin3x=cosx+cos2x+cos3x
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sharadi
Verified answer
Sinx+sin2x+sin3x=cos
x+cos2x+
cos3x
2Sin2xCosx + Sin2x = 2Cos2xCosx + Cos2x
Sin2x(2Cosx +1) = Cos2x(2Cosx +1),
Sin2x(2Cosx +1) - Cos2x(2Cosx +1)= 0
(2Cosx +1)(Sin2x -Cos2x) = 0
2Cosx +1 = 0 или Sin2x -Cos2x = 0
Cosx = -1/2 tg2x = 1
x = +-2π/3 + 2πk , k ∈Z
2x = π/4 + πn , n ∈Z
x = π/8 + πn/2 , n∈Z
6 votes
Thanks 13
elvira1234123
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Answers & Comments
Verified answer
Sinx+sin2x+sin3x=cosx+cos2x+cos3x2Sin2xCosx + Sin2x = 2Cos2xCosx + Cos2x
Sin2x(2Cosx +1) = Cos2x(2Cosx +1),
Sin2x(2Cosx +1) - Cos2x(2Cosx +1)= 0
(2Cosx +1)(Sin2x -Cos2x) = 0
2Cosx +1 = 0 или Sin2x -Cos2x = 0
Cosx = -1/2 tg2x = 1
x = +-2π/3 + 2πk , k ∈Z 2x = π/4 + πn , n ∈Z
x = π/8 + πn/2 , n∈Z