Question

How do you use the angle sum or difference identity to find the exact value of `cos(pi/3)cos(pi/6)+sin(pi/3)sin(pi/6)`?

Answer 1

`sqrt3/2`

Explanation:

Apply the trig identity:
cos (a - b) = cos a.cos b + sin a.sin b
`cos (pi/3 - pi/6) = cos (pi/3).cos (pi/6) + sin (pi/3).sin (pi/6)`
Trig table of special arcs gives:
`cos pi/3 = 1/2`, and `cos (pi/6) = sqrt3/2`
`sin (pi/3) = sqrt3/2`, and `sin (pi/6) = 1/2`
There for,
`cos (pi/3 - pi/6) = (1/2)(sqrt3/2) + (sqrt3/2)(1/2) = (2sqrt3)/4 = sqrt3/2`