How do you express $cos( (15 pi)/ 8 ) * cos (( 15 pi) /8 )$ without using products of trigonometric functions?

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Answer 1 · 2016-03-13T09:08:14

$1/2+1/2cos(pi/4)$

$cos((15pi)/8)*cos((15pi)/8)=cos^2((15pi)/8)$

As $cos2A=2cos^2A-1$ , $cos^2A=1/2+(cos2A)/2$

Hence $cos((15pi)/8)*cos((15pi)/8)=1/2+1/2cos((15pi)/4)$

= $1/2+1/2cos(4pi-pi/4)$

= $1/2+1/2cos(-pi/4)=1/2+1/2cos(pi/4)$

How do you express cos( (15 pi)/ 8 ) * cos (( 15 pi) /8 ) cos( (15 pi)/ 8 ) * cos (( 15 pi) /8 ) without using products of trigonometric functions?