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How do you use the angle sum identity to find the exact value of cos 165?

1 Answer

Nghi N. · Ernest Z.

Apr 25, 2015

#cos (165)= (sqrt3-1)/(2sqrt2)#

Ans: #- (sqrt3 + 1)/(2sqrt2)#

Explanation:

#cos (165)= cos(120+45)#

#cos(165) = cos 120·cos 45 - sin 120·sin 45 = (-1/2)·sqrt2/2 - sqrt3/2·sqrt2/2 = - sqrt2/2 (1/2 + sqrt3/2) = #

#cos (165)= -(sqrt3 + 1)/(2sqrt2)#

Check by calculator.
cos 165 = - 0.97 ; #- (sqrt3 + 1)/(2sqrt2) = - 2.732/2.828 = - 0.97.# OK

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