In a △ABC, if acos2⁡B2+bcos2⁡A2=3c2 then - Infinity Learn by Sri Chaitanya

A
$a, b, c$ are in A.P.
B
$a, c, b$ are in A.P.
C
$a, b, c$ are in G.P.
D
none of these

Solution:

we have ,

$\begin{array}{l} a \cos^{2} \frac{B}{2} + b \cos^{2} \frac{A}{2} = \frac{3 c}{2} \\ \Rightarrow a (1 + \cos B) + b (1 + \cos A) = 3 c \\ \Rightarrow a + b + (a \cos B + b \cos A) = 3 c \\ \Rightarrow a + b + c = 3 c [∵ c = a \cos B + b \cos A] \\ \Rightarrow a + b = 2 c \Rightarrow a, c, b are in A.P. \end{array}$

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