Question

COSA + COSB + Cosc = R + b2 +ce Lab

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Answer 1

Answer:

olution

Here, we will use,<br>

cosA+cosB+cosC = 1+4sin(A/2)sin(B/2)sin(C/2)

<br> Now, <br>

L.H.S. = cosA+cosB+cosC = 1+4sin(A/2)sin(B/2)sin(C/2)

<br>

=1+(4Rsin(A/2)sin(B/2)sin(C/2))/R

<br> Now,

4Rsin(A/2)sin(B/2)sin(C/2) =

inradius

= r

<br> So,

1+(4Rsin(A/2)sin(B/2)sin(C/2))/R = 1+r/R = R.H.S.

<br>