Question 1007381
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Use an addition or subtraction formula to write the expression as a trigonometric function of one number:
cos(3pi/7) cos(2pi/21) + sin(3pi/7) sin(2pi/21)

Find A and B where, cos= pi/A = B/2
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Use the formula 

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

It is well known formula, you can find it in any textbook on trigonometry.

See, for example, the lesson <A HREF=http://www.algebra.com/algebra/homework/Trigonometry-basics/Addition-and-subtraction-formulas.lesson>Addition and subtraction formulas</A> in this site.

By applying this formula, you will get 

{{{cos(3pi/7) cos(2pi/21) + sin(3pi/7) sin(2pi/21)}}} = {{{cos(3pi/7 - 2pi/21)}}} = {{{cos(9pi/21 - 2pi/21)}}} = {{{cos(8pi/21)}}}.

The right side of this chain of equaities is a trigonometric function of one number, so I think it is the answer to the first part of the claim.

Regarding the last part of the claim (the last line), I do not understand what does it mean.
Mathematical texts or texts for students should not contain nonsense like this. It is inappropriate.
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