cos 5pi/12 cos pi/4 + sin5pi/12 sin pi/4

Answer 1

cos(a-b)=cos(a)cos(b) + sin(a)sin(b)

So what you have is

Cos[(5π/12)-(π/4)]

Common denominator would be 12 multiply the top and bottom of π/4 by 3

Cos[(5π/12)-(3π/12)]

Cos(2π/12)

Cos(π/6)=√3/2=0.866