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sin(3x) = 3cos^{2}x.sin(x)-sin^{3}x. Please give me proof for above formula.

sin(3x) = 3cos^{2}x.sin(x)-sin^{3}x.
Please give me proof for above formula.

Grade:12

3 Answers

Raghuvaran varan Chandragiri
37 Points
9 years ago

sin(2x+x)=sin2x.cosx+cos2x.sinx

             =2sinxcosx.cosx+(-2sin^2x)sinx

             =2sinxcos^2+sinx-2sin^3x

            =sinx(2cos^2x+1)-2sin^3x

=sinx(2-2sin^2x+1)-2sin^3x

           =2sinx-2sin^3x+sinx-2sin^3x

                                            = 3sinx-4sin^3x

badapalli Kurmarao
31 Points
9 years ago

sin(2x+x)=sin2x.cosx+cos2x.sinx

 =2sinxcosx.cosx+(-2sin^2x)sinx

=2sinxcos^2+sinx-2sin^3x

 =sinx(2cos^2x+1)-2sin^3x

=sinx(2-2sin^2x+1)-2sin^3x

 =2sinx-2sin^3x+sinx-2sin^3x

 = 3sinx-4sin^3x

 

prasanth battula
37 Points
9 years ago

thank you,you missed putting 1 in the second step in your answer

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