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Math Help - Proof of Isosceles Trapezoid

  1. #1
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    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
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  2. #2
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    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).
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  3. #3
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    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?
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  4. #4
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    Re: Proof of Isosceles Trapezoid

    Yes.
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