show that 4sinxsin(x+pi/3)sin(x+2pi/3)=sin3x

Asked by pooja dev | 20th Nov, 2010, 06:43: PM

Expert Answer:

Dear Student,

Simply expand the terms to:

4sinx(sinx/2 + √3/2cosx)(-sinx/2+ √3/2cosx)

=> sinx (sinx + √3cosx)(-sinx+ √3cosx)

=> sinx (3cos2x – sin2x)

=> sinx (3 – 3sin2x –sin2x)

=> sinx (3 – 4sin2x)

=> 3sinx – 4sin3x

=> sin3x

Regards Topperelearning

Answered by  | 21st Nov, 2010, 12:25: PM

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