Use a sum or difference formula to find the exact value of t

Use a sum or difference formula to find the exact value of the given trigonometric function. Do not use a calculator.

cos

Solution

cos(pi/12) = cos(pi/3 - pi/4)

now use cosine difference formula:

cos(A -B) = coscosB +sinAsinB

cos(pi/3 - pi/4) = cospi/3*cospi/4 + sinpi/3sinpi/4

= (1/2)(1/sqrt2) + (sqrt3/2)(1/sqrt2)

= ( 1 +sqrt3)/2sqrt(2)