Question

If A,B,C,D are the angles of a cyclic quadrilateral, then CosA+CosB+CosC+CosD = ? plss answer​

Answer 1

Answer:

ANSWER

ABCD is a cyclic quadrilateral.

We know that opposite angles of cyclic quadrilateral are supplementary.

∴ A+C=π=180

o

⇒ A=π−C

⇒ cosA=cos(π−C)

⇒ cosA=cosπ.cosC+sinπ.sinC

⇒ cosA=(−1).cosC+0.sinC

⇒ cosA=−cosC

∴ cosA+cosC=0 ----- ( 1 )

∴ B+D=π=180

o

⇒ B=π−D

⇒ cosB=cos(π−D)

⇒ cosB=cosπ.cosD+sinπ.sinD

⇒ cosB=(−1).cosD+0.sinD

⇒ cosB=−cosD

∴ cosB+cosD=0 ---- ( 2 )

Adding ( 1 ) and ( 2 ) we get,

⇒ cosA+cosB+cosC+cosD=0