In any △ABC, if cot⁡A2,cot⁡B2,cot⁡C2 are in A.P., then a, b, c are in

A
A.P.
B
G.P.
C
H.P.
D
none of these

Solution:

We have,

$\cot \frac{A}{2}, \cot \frac{B}{2}, \cot \frac{C}{2}$ are in A.P.

$\begin{array}{l} \Rightarrow 2 \cot \frac{B}{2} = \cot \frac{A}{2} + \cot \frac{C}{2} \\ \Rightarrow 2 \sqrt{\frac{s (s - b)}{(s - a) (s - c)}} = \sqrt{\frac{s (s - a)}{(s - b) (s - c)}} + \sqrt{\frac{s (s - c)}{(s - a) (s - b)}} \end{array}$

$\Rightarrow 2 (s - b) = s - a + s - c \Rightarrow 2 b = a + c \Rightarrow a, b, c$ are in A.P.

In any $△ A B C,$ if $\cot \frac{A}{2}, \cot \frac{B}{2}, \cot \frac{C}{2}$ are in A.P., then $a, b, c$ are in

Solution:

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