Use a cosine sum or difference identity to find the exact va

Use a cosine sum or difference identity to find the exact value.

cos(- pi/12)=

(simplify your answer, including all radicals. Use integers or fractions for any numbers in the expression.)

Solution

cos(-pi/12) = cos(pi/12)     -----> cosx is an even function

Use the formula : cosx = sqrt[ (1+cos2x)/2]

So, cos(pi/12) = sqrt[( 1+cospi/6)/2]

= sqrt[(1 + sqrt3/2)/2]

= sqrt[ (2+ sqrt3)]/2