If A , B , C ,D are angles of a cyclic quadrilateral , then prove that cosA + cosB+cosC+cosD=0.

If A+B+C=pi . Then prove that cosA=-cos(B+C)

Prove that any outer angle of a cyclic quadrilateral is equal to the inner angle at the opposite vertex.

Prove that any outer. angle of a cyclic quadrilateral is equal to the interior angle, at the opposite vertex.

Let A subset B, C subset D , then prove that A xx C subset B xx D

If c, d are the roots of the equation (x-a) (x-b) - k=0 , then prove that a, b are the roots of the equation (x-c) (x-d) + k= 0

Prove that cosAsin(B-C)+cosBsin(C-A)+cosCsin(A-B)=0

If A,B,C are the angle of a triangle then the value of determinant |(sin2A,sinC,sinB),(sinC,sin2B,sinA),(sinB,sinA,sin2C)| is a) pi b) 2lambda c)0 d)None of these