Find the exact value of Cos 7pie/12

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