How do you use the half-angle identity to find the exact value of cos(-pi/12)?

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How do you use the half-angle identity to find the exact value of cos(-pi/12)?

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Answer 1 · 2015-09-22T13:48:30

#sqrt(2+sqrt3)/2#

Explanation:

#cos(-pi/12)=cos(pi/12)##as# #cos(x)# #is# #a# #even function# # f(x)=f(-x)#
#costheta=sqrt((1+cos2theta)/2)#
#=>cos(pi/12)=sqrt((1+cos(pi/6))/2)=sqrt((1+sqrt3/2)/2)=sqrt(2+sqrt3)/2#

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How do you use the half-angle identity to find the exact value of cos(-pi/12)?

1 Answer

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