7pi/12 = 3pi/12 + 4pi/12 = pi/4 + pi/3 Both pi/4 and pi/3 are known unit circle values.

So we can use the sum formula :cos(a + b) = cos(a)cos(b) - sin(a)sin(b)

cos( 7pi/12 )= cos( 3pi/12 + 4pi/12 )=cos( pi/4 + pi/3 )=cos(pi/4)*cos(pi/3)-sin(pi/4)*sin(pi/3)= [sqrt(2)/2]*[ 1/2 ] - [sqrt(2)/2]*[ sqrt(3)/2 ] = [ sqrt(2)/4 ] - [ sqrt(6)/4 ] = [ sqrt(2) - sqrt(6) ] / 4

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