Question 979506


Find the exact value by using a half-angle identity. (4 points) 
{{{cos(5pi/12)}}}.

 
Here is my work, can someone please check to see if I did it right? 


{{{cos ((5pi/6)/2)}}} = +/- {{{sqrt( (1+cos (5pi/6))/2 )}}}     correct


{{{cos(5pi/6)}}} = {{{-sqrt(3)/2}}}                                      correct


{{{cos (5pi/12)}}} = +/- {{{sqrt( (2/2-sqrt(3)/2)/2 )}}}                       correct


{{{cos (5 pi/12)}}} = +/- {{{sqrt( ((2-sqrt(3))/2)/2 )}}}                   correct


{{{cos (5pi/12)}}} = {{{sqrt( (2-sqrt(3))/4 )}}}                               correct



EVERYTHING IS CORRECT.
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You can write the last expression as 


{{{cos (5pi/12)}}} = {{{sqrt(2-sqrt(3))/2}}}.