Math, asked by fahimasaadatmulla, 1 month ago

prove that sin 3x=3 sin x-4 sin 3x​

Answers

Answered by diwanamrmznu
2

Answer: -

LHS

 \implies \sin \: 3x \\  \\  \implies \sin \:( 2x + x) \\  \\  \implies \sin \: 2x. \cos \: x +  \cos \:2 x. \sin \: x \\  \\  \implies 2 \sin \: x \cos \: x. \cos \: x + (1 - 2 \sin \:  {}^{2} x) \sin \: x \\  \\  \implies \: 2 \sin \: x. \cos {}^{2} x +  \sin \: x - 2 \sin {}^{3} x \\  \\  \implies \: 2 \sin \: x(1 -  { \sin}^{2} x) +  \sin \: x - 2 \sin \:  {}^{3} x \\  \\  \implies \: 2 \sin \: x - 2 \sin {}^{3} x +  \sin \: x - 2  { \sin}^{3} x \\  \\  \implies \: 3 \sin \: x -  \: 4 \sin {}^{3} x

hence proved

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formula use:

 \implies \pink{ \sin \: (a + b) =  \sin \: a \cos \: b +  \cos \: a \sin \: b} \\  \\  \implies \pink{ \cos \: 2x = 1 - 2 \sin {}^{2} x}

Answered by meerakambad
3

Step-by-step explanation:

sin3x=sin ( 2x + x )

=sin2xcosx + cos 2x sin x

=2sinx cosx cosx + ( 1 − 2 sin²x )sinx

=2sinx( 1 − sin²x ) + sinx − 2sin 3x

=3sinx − 4sin 3x

I'm good

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