If in triangle ABC,with usual notations,a cdo | vedclass

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(C) Given the equation: $a \cdot \cos^2 \frac{C}{2} + c \cdot \cos^2 \frac{A}{2} = \frac{3b}{2}$ Using the identity $\cos^2 	heta = \frac{1 + \cos(2\

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$a, b, c$ are in $A$.$P$.

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(C) Given the equation: $a \cdot \cos^2 \frac{C}{2} + c \cdot \cos^2 \frac{A}{2} = \frac{3b}{2}$ Using the identity $\cos^2 	heta = \frac{1 + \cos(2	heta)}{2}$,we get: $a \left( \frac{1 + \cos C}{2} ight) + c \left( \frac{1 + \cos A}{2} ight) = \frac{3b}{2}$ Multiplying by $2$: $a(1 + \cos C) + c(1 + \cos A) = 3b$ $a + a \cos C + c + c \cos A = 3b$ Using the projection formula $b = a \cos C + c \cos A$: $a + c + b = 3b$ $a + c = 2b$ This condition implies that $a, b, c$ are in $A$.$P$.

If in $\triangle ABC$,with usual notations,$a \cdot \cos^2 \frac{C}{2} + c \cdot \cos^2 \frac{A}{2} = \frac{3b}{2}$,then

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