Prove that `cosA+cosB+cosC=1+r/R`

If A+B+C = pi , prove that : cosA- cosB - cosC = 1-4sinA//2cosB//2cosC//2 .

In DeltaABC , Prove that: cosA+cosB+cosC=1+4sinA/2sinB/2sinC/2

In DeltaABC, (b+c)/(11) = (c+a)/(12)=(a+b)/(13) , prove that: cosA:cosB:cosC=?

If A+B+C=pi , prove that : cosA + cosB-cosC=4cos(A/2) cos(B/2) sin(C/2) -1

If A+B+C+D = 2pi , prove that : cosA +cosB+cosC+cosD=4 cos( (A+B)/2) cos((B+C)/(2) )cos( (C+A)/2)

If A+B+C=pi , prove that : sinA cosB cosC +sinB cosC cosA + sinC cosA cosB = sinA sinB sinC .

If A,B,C and D are the angles of cyclic quadrilateral, prove that: i) cosA + cosB+cosC+cosD ii) cos(180^(@)-A)+cos(180^(@)+B)+cos(180^(@)+C)-sin(90^(@))

If A+B+C=pi , prove that : cosA sinB sinC +cosB sinC sinA+cosC sinA sinB=1+cosA cosB cosC .

Prove that (sin(B-C))/(cosB cosC)+(sin(C-A))/(cosC cosA)+(sin(A-B))/(cosA cosB) =0 .