Question

If ABCD is a cyclic quadrilateral, then find the value of cos A cos B - cos C cos D.

Answer 1

b'

ABCD is a cyclic quadrilateral.

$A+C={180}^o$ and $B+D={180}^o$

Now,

$\cos A\cos B-\cos C\cos D=\cos A\cos B-\cos ({180}^o-A)\cos ({180}^o-B)$

$=\cos A\cos B-(-\cos A)(-\cos B)=\cos A\cos B-\cos A\cos B=0$

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