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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
= .
It is well known formula, you can find it in any textbook on trigonometry.
See, for example, the lesson Addition and subtraction formulas in this site.
By applying this formula, you will get
= = = .
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.