Answer:
The value is ((square root 2)- (square root 6))/4
Step-by-step explanation:
We can find the value by breaking up the cos (7pi/12) into
cos (4pi/12 + 3pi/12)
This is the same thing as
cos (pi/3 + pi/4)
You can then rewrite that as
cos(pi/3) * cos(pi/4) - sin(pi/3) * sin(pi/4)
Then solve for each value
1/2 * ((square root 2)/2) - ((square root 3)/2) * ((square root 2)/2)
Multiply each value that should be together
((square root 2)/4) - ((square root 6)/4)
Common denominators allow the answer to be further simplified to
((square root 2)- (square root 6))/4
