(cos(a+15))^2+(sin(a-15))^2+sinacos(a-180)
=[1+cos(2a+30)]/2 +[1-cos(2a-30)]/2-sina cosa
=1/2+cos(2a+30)/2+1/2-cos(2a-30)/2-sin2a/2
=1+cos2acos30-sin2asin30-cos2acos30-sin2asin30
-sin2a/2
=1-2sin2asin30-sin2a/2
=1-sin2a-sin2a/2
=1-sin2a/2