Question

in cyclic quadrilateral ABCD, the value of sinA/2 + sinB/2 - cosC/2 cosD/2 =

Answer 1

If it's a cyclic quadrilateral
A+C=B+D=180º
A=180º-C
B=180–D

\[ \sin \frac{A}{2}+\sin \frac{B}{2} -\cos \frac{C}{2}-\cos \frac{D}{2}\]
\[= \sin \frac{180 -C}{2}+\sin \frac{180-D}{2} -\cos \frac{C}{2}-\cos \frac{D}{2}\]
\[= \sin \Big( 90-\frac{C}{2} \Big) +\sin\Big( 90-\frac{D}{2}\Big) -\cos \frac{C}{2}-\cos
\frac{D}{2}\]
\[=\cos \frac{C}{2}+\cos \frac{D}{2}-\cos \frac{C}{2}-\cos \frac{D}{2}\]
\[=0\]

Answer 2

*if it's not crossed