How do you find the exact value of $cos ((7pi)/12)$ ?

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Answer 1 · 2016-05-27T12:25:21

Exactly $-(sqrt 3-1)/(2sqrt 2) =-0.25882$ , nearly

$cos((7pi)/12)$

$=cos(pi/3+pi/4)$

$=cos (pi/3) cos (pi/4) - sin ((pi/3) sin (pi/4)$

$=(1/2)(1/sqrt 2)-(sqrt 3/2)(1/sqrt 2)$

$=-(sqrt 3-1)/(2 sqrt 2)$

How do you find the exact value of cos ((7pi)/12)cos ((7pi)/12)?