Express the value of cosine of 7pi/12 using the angles pi/3 and pi/4

We'll write the angle 7pi/12 as being the summation of the
angles pi/3 and pi/4.

7pi/12 = pi/3 +
pi/4

We'll apply cosine function both
sides:

cos (7pi/12) = cos(pi/3 +
pi/4)

cos(pi/3 + pi/4) = cos (pi/3)*cos (pi/4) - sin
(pi/3)*sin(pi/4)

cos(pi/3 + pi/4) = (1/2)*(sqrt2/2) -
(sqrt3/2)*(sqrt2/2)

cos(pi/3 + pi/4) =
(sqrt2)*(1-sqrt3)/4

The requested value of
cos (7pi/12) is: cos (7pi/12) =
(sqrt2)*(1-sqrt3)/4.