SOLUTION: 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, co

Algebra ->  Trigonometry-basics -> SOLUTION: 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, co      Log On


   

Question 1007381: 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
I cannot find the answer for this one.

Answer by ikleyn(52799) About Me  (Show Source):
You can put this solution on YOUR website!
.
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
------------------------------------------------------------------- 
Use the formula 

cos%28alpha%29%2Acos%28beta%29+%2B+sin%28alpha%29%2Asin%28beta%29 = cos%28alpha-beta%29.

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 

cos%283pi%2F7%29+cos%282pi%2F21%29+%2B+sin%283pi%2F7%29+sin%282pi%2F21%29 = cos%283pi%2F7+-+2pi%2F21%29 = cos%289pi%2F21+-+2pi%2F21%29 = cos%288pi%2F21%29.

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.