Use an identity to find the exact value of cos pi12 Please s

Use an identity to find the exact value of cos pi/12. -Please state the identity used, thanks in advance.

Solution

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

Now use identity: cos(A-B) = cosAcosB +sinAsinB

cos(pi/12) = cos(pi/3 -pi/4) = cospi/3*cospi/4 +sinpi/3sinpi/4

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

= ( 1+sqrt3)/2sqrt2