lf A,B,C and D are the angles of a cyclic quadrilateral, then cos A + cos B + cos C + cos D is equal to

lf A,B,C and D are the angles of a cyclic quadrilateral, then cos A + cos B + cos C + cos D is equal to

  1. A

    2 (cos A + cos C)

  2. B

    2 (cos A + cos B)

  3. C

    2 (cos A + cos D)

  4. D

    0

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    Solution:

    Given that, ABCD is a cyclic quadrilateral.

     So, A+C=180A=180CcosA=cos180C=cosCcosA+cosC=0---i Similarly, cosB+cosD=0----ii

    On adding Eqs. (i) and (ii), we get
    cosA + cosB + cosC + cosD =0 

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