JEE Advance - Mathematics (2000 - No. 16)
In any triangle $$ABC,$$ prove that
$$$\cot {A \over 2} + \cot {B \over 2} + \cot {C \over 2} = \cot {A \over 2}\cot {B \over 2}\cot {C \over 2}.$$$
This statement is not generally true for all triangles.
The identity holds true because A + B + C = 180 degrees, and using trigonometric identities for cotangent of half-angles and the fact that cot(90-x) = tan(x).
The identity is true only for equilateral triangles.
The identity is a consequence of the Law of Sines.
The identity is a consequence of the Law of Cosines.
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