Find the exact value of the expression Use a calculator to s

Find the exact value of the expression. Use a calculator to support your result. cos^2 (-165 degrees)

cos^2(-165) = cos^2(165) cos is an even function

Now cos(165) = cos(180 -15) = -cos15

So,cos^2(-165) = cos^15

Use half angle formula : cos(x) = sqrt[(1+cos2x)/2]

So, cos15 = sqrt[( 1+cos30)/2]

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

= sqrt[(2+sqrt3)/4)]

= sqrt[(2+sqrt3)]/2

So, cos^2(-165) = cos^15 = (2+sqrt3]/4