Question

How do you find the exact value of cos(pi/3)cos(5pi/12)-sin(pi/3)sin(5pi/12)?

Answer 1

`-sqrt2/2`

Explanation:

Apply the trig identity:
cos a.cos b - sin a.sin b = cos (a + b)
`cos (pi/3).cos ((5pi)/12) - sin ((5pi)/12).sin (pi/3) =`
`= cos (pi/3 + (5pi)/12) = cos ((9pi)/12) = cos ((3pi)/4) = -sqrt2/2`