In any Δ ABC, prove that
(i)R r (sin A + sin B + sin C) = Δ
(ii)a cos B cos C + b cos C cos A + c cos A cos B = 
(iii) 
+ 
+ 
= 
.
(iv)cos 2 
+ cos 2 
+ cos 2 
= 2 + 
(v)a cot A + b cot B + c cot C = 2(R + r)
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
(i)L.H.S. = Rr(sin A + sin B + sin C)
= Rr 
r = 
= 
= rs = Δ
(ii) L.H.S. = a cos B cos C + cos A(b cos C + c cos B)
= a[cos B cos C + cos A]
= a[cos B cos C – cos (B + C)]
= a sin B sin C
= a. 
. 
= 
= 
= 
(iii) L.H.S. = 
= 
= 
= 
(iv) L.H.S. {k = 
(1 + cos A + 1 + cos B + 1 + cos C)
= 
= 2 + 
= 2 + 
(v) L.H.S. {k = 
= 2R 
= 2R + 2r = 2 (R + r)
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