Trigonometric twist
Geometry
Level
3
If b + c = 3a, find the value of Cot (B/2)Cot(C/2).
The answer is 2.
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1 solution
Cot(B/2)= √(((s) (s-b)) /((s-a)(s-c)))
Cot(C/2)= √(((s) (s-c)) /((s-a) (s-b)))
Where s = (a + b + c) /2
Therefore
Cot(B/2)Cot(C/2) = s/(s-a)
b + c = 3a
a + b + c = 4a
2s = 4a
s = 2a
s/(s-a) = 2a/(2a - a) = 2a/a=2