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July 2022
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2sin x=1 - cos2x решите плз
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Verified answer
2sinx=1-cos2x
2sinx=cos²x+sin²x-(cos²x-sin²x)
2sinx=cos²x+sin²x-cos²x+sin²x
2sinx=2sin²x |:2
sinx=sin²x
sinx-sin²x=0
sinx(1-sinx)=0
sinx=0 или 1-sinx=0
x₁=πn, n∈Z
sinx=1
x₂=π/2+2πn, n∈Z
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Answers & Comments
Verified answer
2sinx=1-cos2x2sinx=cos²x+sin²x-(cos²x-sin²x)
2sinx=cos²x+sin²x-cos²x+sin²x
2sinx=2sin²x |:2
sinx=sin²x
sinx-sin²x=0
sinx(1-sinx)=0
sinx=0 или 1-sinx=0
x₁=πn, n∈Z sinx=1
x₂=π/2+2πn, n∈Z