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  • From (1),Example 9. If ABCD is a cyclic quadrilateral, prove thatcos A + cos B + cos C + cos D = 0.Solution. Since ABCD is a cyclic quadrilateralA+ C = 180° and B + D = 180°L.H.S. = cos A + cos B + cos C + cos D= cos A + cos B + cos (180° - A) + cos (1

From (1),Example 9. If ABCD is a cyclic quadrilateral, prove thatcos A + cos B + cos C + cos D = 0.Solution. Since ABCD is a cyclic quadrilateralA+ C = 180° and B + D = 180°L.H.S. = cos A + cos B + cos C + cos D= cos A + cos B + cos (180° - A) + cos (180°-B)= cos A + cos B - cos A - cos B = 0 = R.H.S.Example 10. In any quadrilateral ABCD, prove thatsin (A+B) + sin (C+D) = 0cos (A + B) = cos (C+D)Solution. Since ABCD is a quadrilateralA + B + C + D = 2 = A + B = 27 - (C+D)?

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