cos^2 150-(sin 70 cos 40-cos70 cos(90-40))^2

cos^2 150-(sin 70 cos 40-cos 70 sin 40)^2

cos^2 150-(sin 30)^2=cos^2 (180-30)-(sin 30)^2=cos^2 30-sin^2 30=3/4-1/4=2/4=1/2