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If A,B,C,D is a cyclic quadrilateral,then the value of cosA-cosB+cosC-cosD=

If A,B,C,D is a cyclic quadrilateral,then the value of cosA-cosB+cosC-cosD=

Grade:11

2 Answers

Saurabh Koranglekar
askIITians Faculty 10335 Points
4 years ago
Dear student

The question seems to be incomplete, many values can be obtained based on the limited information, kindly upload complete question

Regards
Samyak Jain
333 Points
4 years ago
ABCD is a cyclic quadrilateral. And we know that the sum of opposite angles of a cyclic quadrilateral is 180\degree.
\therefore  A + C  =  180\degree  …. (1)  and   B + D  =  180\degree  …. (2)
From (1), A  =  180\degree  –  C   \Rightarrow   cosA = cos(180\degree –  C)   \Rightarrow   cosA = – cosC
or cosA + cosC = 0        ...(3).
From (2), B  =  180\degree  –  D   \Rightarrow   cosB = cos(180\degree –  D)   \Rightarrow   cosB = – cosD
or cosB + cosD = 0        ...(4).
Subtract (4) from (3).
(cosA + cosC) – (cosB + cosD) = 0  i.e.
 cosA – cosB + cosC – cosD = 0.

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