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

Question

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!!

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Answer 1 · 2018-05-06T22:36:02

See below

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#