Question 1171121
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Use one of the basic Trigonometry formulas for the product of sine functions


    {{{sin(a)*sin(b)}}} = {{{(1/2)*(cos(a-b) - cos(a+b))}}}.


In your case  a = 3x;  b = x;  therefore


    sin(3x)*sin(x) = {{{(1/2)*(cos(3x-x) - cos(3x+x))}}} = {{{(1/2)*cos(2x)}}} - {{{(1/2)*cos(4x)}}},


exactly as requested.
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Solved.