Question

8.
If A, B, C, D are angles of quadrilateral, then prove the
cos A+B÷2​

Answer 1

Answer:

We know that the opposite angles of a cyclic quadrilateral are supplementary,

i.e., A+C=π and B+D=π.

Therefore,

A=π−C and B=π−D

⇒ cosA=cos(π−C)=−cosC

and cosB=cos(π−D)=−cosD

∴ cosA+cosB+cosC+cosD=−cosC−cosD+cosC+cosD=0

Ans: 0