what is the exact value of sin^2 pi/6-2 sin pi/6 cos pi/6 +cos^2 (-pi/6)?

Question

a) 2- sqrt 3
b) 2- sqrt 3/ 2
c) 2+ sqrt 3/2
d) 2+ sqrt 3

I am not sure how to work this out and would appreciate you how to show me the process. Thank you in advanced!!!!!!!

Answer 1

sin pi/6 = sin 30 deg = 1/2

cos pi/6 = .5 sqrt 3

cos -x = cos x
so

1/4 - .5 sqrt 3 + 3/4

1 - .5 sqrt 3

(2 - sqrt 3 ) / 2