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Prove that the equation is an identity.

 

   sin3x =sin(x)*( 3cos^2 x - sin^2 x )

 Aug 7, 2014

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 #1
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 sin3x =sin(x)*( 3cos^2 x - sin^2 x )

sin3x =

sin (2x + x) =

sin2xcosx + cos2xsinx =

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

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

3sinxcos^2x - sin^3x =

sinx*(3cos^2x - sin^2x) ......and this equals the right hand side......

 

 Aug 7, 2014
 #1
avatar+130511 
+10
Best Answer

 sin3x =sin(x)*( 3cos^2 x - sin^2 x )

sin3x =

sin (2x + x) =

sin2xcosx + cos2xsinx =

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

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

3sinxcos^2x - sin^3x =

sinx*(3cos^2x - sin^2x) ......and this equals the right hand side......

 

CPhill Aug 7, 2014
 #2
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Thank you! 

 Aug 7, 2014

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