With usual notations,in Delta ABC,if b cos ^{ | vedclass

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(A) Given $b \cos ^{2} \frac{C}{2}+c \cos ^{2} \frac{B}{2}=\frac{3 a}{2}$.Using the identity $\cos ^{2} 	heta = \frac{1+\cos 2	heta}{2}$,we have:$b

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

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(A) Given $b \cos ^{2} \frac{C}{2}+c \cos ^{2} \frac{B}{2}=\frac{3 a}{2}$.Using the identity $\cos ^{2} 	heta = \frac{1+\cos 2	heta}{2}$,we have:$b \left( \frac{1+\cos C}{2} ight) + c \left( \frac{1+\cos B}{2} ight) = \frac{3 a}{2}$.Multiplying by $2$ on both sides:$b(1+\cos C) + c(1+\cos B) = 3a$.$b + b \cos C + c + c \cos B = 3a$.Rearranging terms:$(b \cos C + c \cos B) + b + c = 3a$.By the projection rule,$b \cos C + c \cos B = a$,so:$a + b + c = 3a$.$b + c = 2a$.This implies that $b, a, c$ are in $A$.$P$.

With usual notations,in $\Delta ABC$,if $b \cos ^{2} \frac{C}{2}+c \cos ^{2} \frac{B}{2}=\frac{3 a}{2}$,then

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