If in a [ ABC] [a, ^2( C 2 ) + c, ^2( A 2 ) = 3b 2,] then the sides a, b and c :

Question

If in a $$\Delta ABC$$ $$a\,{\cos ^2}\left( {{C \over 2}} \right) + c\,{\cos ^2}\left( {{A \over 2}} \right) = {{3b} \over 2},$$ then the sides $a, b$ and $c$ :

Accepted Answer

If $$a\,{\cos ^2}\left( {{C \over 2}} \right) + c\,{\cos ^2}\left( {{A \over 2}} \right) = {{3b} \over 2}$$

$$a\left[ {\cos C + 1} \right] + c\left[ {\cos A + 1} \right] = 3b$$

$$\left( {a + c} \right) + \left( {a\cos C + c\cos \,B} \right) = 3b$$

$a + c + b = 3b$ or $a + c = 2b$

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

Solutions · 1