Question 1107683
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<pre>
  {{{sinxcos^3x-cosxsin^3x=(1/4)(sin4x)}}} = {{{sin(x)*cos(x)*(cos^2(x)-sin^2(x))}}} = 


     Use the basic trigonometric formulas  sin(x)*cos(x) = {{{(1/2)*sin(2x)}}},   cos^2(x)-sin^2(x) = cos(2x)  to get


= {{{(1/2)*sin(2x)*cos(2x)}}} =  //use again  sin(2x)*cos(2x) = {{{(1/2)*cos(4x)}}}  to get //   = {{{(1/4)*cos4x)}}}.


That's all.
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