sin 3x= 3 sin x - 4 sin3
x
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Since the angle sum formula of sine is:sin(α+β)=sinαcosβ+cosαsinβ ,and the double angle formula of cosine:cos(2α)=cos2α−sin2α=2cos2α−1=1−2sin2αthen:sin(3x)=sin(2x+x)=sin(2x)cosx+cos(2x)sinx==(2sinxcosx)⋅cosx+(1−2sin2x)sinx==2sinxcos2x+sinx−2sin3x= =2sinx(1−sin2x)+sinx−2sin3x= =2sinx−2sin3x+sinx−2sin3x= =3sinx−4sin3x
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your answer is here
Since the angle sum formula of sine is:sin(α+β)=sinαcosβ+cosαsinβ ,and the double angle formula of cosine:cos(2α)=cos2α−sin2α=2cos2α−1=1−2sin2αthen:sin(3x)=sin(2x+x)=sin(2x)cosx+cos(2x)sinx==(2sinxcosx)⋅cosx+(1−2sin2x)sinx==2sinxcos2x+sinx−2sin3x= =2sinx(1−sin2x)+sinx−2sin3x= =2sinx−2sin3x+sinx−2sin3x= =3sinx−4sin3x
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shekhawatrahul603:
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