Question 1144154
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First,   sin(x/2)cos(x/2) = {{{(1/2)*sin(x)}}}.


Second,  1-2sin^2(x/2)  = cos(x).


Therefore,  sin(x/2)cos(x/2)(1-2sin^2(x/2)) = {{{(1/2)*sin(x)*cos(x)}}} = {{{(1/4)*sin(2x)}}}.    <U>ANSWER</U>
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You need to know basic Trigonometry formulas for multiple arguments &nbsp;(for double arguments, &nbsp;in this case).


See the lesson

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Trigonometry-basics/Compendium-of-Trigonometry-Formulas.lesson>FORMULAS FOR TRIGONOMETRIC FUNCTIONS</A> 

in this site.