Question

if ABCD is a cyclic quadrilateral, then find the value of cosA+cosB+cosC+cosD.

Answer 1

Answer:

As A, B, C, D are the vertices of CyQuad ABCD,

A+C=180° and B+D=180°

By the rules of *associated angles*, we can write,

CosC=Cos(2x90-A)= -CosA.....(1)

We can apply the same process on CosB or CosD......

Then we shall get,

CosB=-CosD................................ (2)

So, in L. H. S.

CosA+CosB+CosC+CosD

=CosA-CosD-CosA+CosD........ From 1&2

=0

Hence, L.H.S=R.H.S., |PROVED|