Question 1067701
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Can somebody help me by writing 4*cos(2*theta)*sin(4*theta) as a sum or difference? Ty.
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<pre>
There is a general formula of Trigonometry

{{{sin(alpha)*cos(beta) = (1/2)*(sin(alpha-beta) + sin(alpha+beta))}}}.


See any serious textbook in Trigonometry or the lessons

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

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Trigonometry-basics/Product-of-trigonometric-functions.lesson>Product of trigonometric functions</A>

in this site. 


This formula is <U>FUNDAMENTAL</U>, which means <U>"everybody must know it"</U>.


According to this formula,

{{{4*cos(2*theta)*sin(4*theta)}}} = {{{4*(1/2)*(sin(4*theta-2*theta) + sin(4*theta+2*theta))}}} = {{{2*sin(2*theta) + 2*sin(6*theta)}}}.
</pre>

<U>Answer</U>.   {{{4*cos(2*theta)*sin(4*theta)}}} = {{{2*sin(2*theta) + 2*sin(6*theta)}}}.