cos (3pi/7) cos (2pi/21)+ sin (3pi/7) sin (2pi/21)= cos (pi/A)= B/2

A=

B=

cos (3pi/7) cos (2pi/21)+ sin (3pi/7) sin (2pi/21)= cos (pi/A)= B/2

A=

B=

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Dalia,

There is a trigonometric identity (angle sum or angle difference) for cosine that looks like this:

cos(x-y) = cos(x)cos(y) + sin(x)sin(y)

In your example, x=3pi/7 and y=2pi/21

Therefore, we can rewrite the whole expression as:

cos(3pi/7 - 2pi/21) which = cos(9pi/21 - 2pi/21) = cos(7pi/21) = cos(pi/3) = 1/2

In your case, cos(pi/A)=cos(pi/3) so A=3 and B/2 = 1/2 so B=1.

Does that make sense? Let me know if you have any further questions!

-Ryan