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

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

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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.