cos^2(a+15)+sin^2(a-15)+sin(a+180)cos(a-180)
=cos^2(a+15)+sin^2(a+15)-sin^2(a+15)+sin^2(a-15)+sinacosa
=1+[sin^2(a-15)-sin^2(a+15)]+sinacosa
=1+[sin(a-15)+sin(a+15)][sin(a-15)-sin(a+15)]+sinacosa
=1+[2sinacos15]*[2cosa*sin(-15)]+sinacosa
=1-sin2a*sin30+(1/2)*sin2a
=1-(1/2)*sin2a+(1/2)*sin2a
=1