Hello,

We know that cos(-x)=cos(x)

Thus cos(-pi/12)=cos(pi/12).

pi/12=(pi/6)/2.

--> cos(-pi/12)=cos((1/2) pi/6)

We know that cos(2x)=2cosē(x)-1. Then cos(x)=2cosē(x/2)-1 --> cos(x/2)=+ or - sqrt[(cos(x)+1)/2]

therefore cos(-pi/12)=+ or - sqrt[(cos(pi/6)+1)/2]

Since -pi/12 is in the fourth quadrant, the cosine is positive.

--------> cos(-pi/12)=sqrt[(cos(pi/6)+1)/2]

(and you should know cos(pi/6))

cos(-pi/12)=sqrt(sqrt(3)+2)/2