[sin(180-a) x cos(90-a) - 1]/cos(-a) = [sin(a) x sin(a) - 1]/(-cos(a)) = [sin^2(a) -1]/(-cos(a)) = [-cos^2(a)]/(-cos(a)) = cos(a)
formula used sin(180-a) = sin(a) cos(90-a) = sin(a) cos(-a) = -cos(a) sin^2(a) + cos^2(a) = 1 all of these are easily proved by the unit circle. you might find someone to explain this. it will be very handy.
