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half angle trigonometry formula

given cos (a)=4/5 and 3pi/2<a<2pi. 
Find the exact value of cos (a/2)
 
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1 Answer

cos(a) = 2cos2(a/2) - 1
Since a/2 in the second quadrant,
cos(a/2)
= -sqrt[(1/2)(1+cos(a))]
= -sqrt[(1/2)(1+4/5)]
= -3sqrt(10)/10 <==Answer