Proof of Isosceles Trapezoid

Hi,

I've been racking my head about trying to do the following problem, but am unable to solve it:

"Quadrilateral ABCD is an isosceles trapezoid with AB parallel to CD. Find the value of P = cos(A/2) * cos(B/2) + cos(C/2) * cos(D/2)"

I started off with A+D = 180, and tried taking the sin and cos of both sides, but not sure where to continue after that.

Thanks

Re: Proof of Isosceles Trapezoid

Replace cos(B/2) with cos(A/2) and cos(D/2) with cos(C/2). Then replace cos(C/2) with cos((π - A)/2).

Re: Proof of Isosceles Trapezoid

Thanks. So I end up getting (Sin (A/2))^2 + (cos(A/2))^2, which basically equals 1. Is this correct?

Re: Proof of Isosceles Trapezoid