Simplify, evaluate if possible using the unit circle: cos(pi/9)cos(pi/18)-sin(pi/9)sin(pi/18) ?

Simplify, evaluate if possible using the unit circle:
cos(pi/9)cos(pi/18)-sin(pi/9)sin(pi/18)
I can put this in all sorts of formats using half and double angle formulas, but I don't know what is the "most simple" or how to evaluate it using the unit circle. Help?
Thanks!!

1 Answer
May 6, 2018

See below

Explanation:

Most simple technique would be to recognize that this is the cosine sum identity:

So:
cos(pi/9)cos(pi/18)-sin(pi/9)sin(pi/18)= cos(pi/9+pi/18)

cos(pi/6)= sqrt3/2