Question

How do you use the sum or difference identities to find the exact value of `cos(-pi/12)`?

Answer 1

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

Explanation:

As `pi/4-pi/3=-pi/12`, we can use here the difference identity for cosine ratio. According to this

`cos(A-B)=cosAcosB+sinAsinB`

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

= `cos(pi/4)cos(pi/3)+sin(pi/4)sin(pi/3)`

= `1/sqrt2xx1/2+1/sqrt2xxsqrt3/2`

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