Question

How do you find the exact functional value cos 23pi/12 using the cosine sum or difference identity?

Answer 1

Find `cos ((23pi)/12)`

Ans:`(sqrt2 - sqrt6)/4`

Explanation:

`cos ((23pi)/12) = cos (-pi/12 + 2pi) = cos pi/12`
Apply the trig identity: cos (a + b) = cos a.cos b - sin a.sin b
`cos pi/12 = cos (pi/3 - pi/4) = cos pi/3.cos pi/4 - sin pi/3sin pi/4`
Trig table gives:
`cos (pi/3) = 1/2` ; `cos (pi/4 ) = sqrt2/2`
`sin (pi/3) = sqrt3/2`; `sin (pi/4) = sqrt2/2`

`cos ((23pi)/12) = (1/2)(sqrt2/2) - (sqrt3/2)(sqrt2/2)`=

`= (sqrt2 - sqrt6)/4`