Question #837e8

1 Answer
turksvids
Dec 23, 2017

#sqrt(2-sqrt(2))/2#

Explanation:

The half-angle formula for cosine is: #cos(x/2)=\pmsqrt((1+cos(x))/2)#

Since #(3pi)/8# is in QI we know its cosine is positive. We also know that #(3pi)/8=((3pi)/4)/2#, so #x=(3pi)/4# for this problem:

#cos((3pi)/8)=sqrt((1+cos((3pi)/4))/2)#
#=sqrt((1+(-sqrt(2)/2))/2)#
#=sqrt(((2-sqrt(2))/2)/2)#
#=sqrt((2-sqrt(2))/4)#
#=sqrt(2-sqrt(2))/2#

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