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

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

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Here, we will use,
`cosA+cosB+cosC = 1+4sin(A/2)sin(B/2)sin(C/2)`
Now,
`L.H.S. = cosA+cosB+cosC = 1+4sin(A/2)sin(B/2)sin(C/2)`
`=1+(4Rsin(A/2)sin(B/2)sin(C/2))/R`
Now, `4Rsin(A/2)sin(B/2)sin(C/2) = `inradius` = r`
So, `1+(4Rsin(A/2)sin(B/2)sin(C/2))/R = 1+r/R = R.H.S.`
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