Question

Cos(7pi/12) + cos(pi/12) =

a. 0
b. .35
c. .71
d. -.71
cos(7pi/12) - cos(pi/12) =
a. 0
b. .65
c. -.54
d. -1.22

Answer 1

The value of cos(7pi/12) + cos(pi/12) is 0.71 and the value of cos(7pi/12) - cos(pi/12) is also 0.71.

Step-by-step explanation:

To find the values of cos(7pi/12) + cos(pi/12) and cos(7pi/12) - cos(pi/12), we can use the trigonometric identity: cos(a) + cos(b) = 2 cos((a+b)/2) cos((a-b)/2).

In the first equation, cos(7pi/12) + cos(pi/12), the values of a and b are 7pi/12 and pi/12 respectively. Plugging these values into the identity, we have: cos(7pi/12) + cos(pi/12) = 2 cos((7pi/12 + pi/12)/2) cos((7pi/12 - pi/12)/2) = 2 cos(8pi/24) cos(6pi/24) = 2 cos(pi/3) cos(pi/4) = 2 * (1/2) * (sqrt(2)/2) = sqrt(2)/2.

Therefore, the value of cos(7pi/12) + cos(pi/12) is 0.71.

Now, let's solve the second equation, cos(7pi/12) - cos(pi/12). Using the same trigonometric identity, we have: cos(7pi/12) - cos(pi/12) = 2 cos((7pi/12 + pi/12)/2) cos((7pi/12 - pi/12)/2) = 2 cos(8pi/24) cos(6pi/24) = 2 cos(pi/3) cos(pi/4) = 2 * (1/2) * (sqrt(2)/2) = sqrt(2)/2.

Therefore, the value of cos(7pi/12) - cos(pi/12) is 0.71.