JEE Main 2019Properties of TriangleProperties of TriangleEasyQuestionIf in a ΔABC\Delta ABCΔABC a cos2(C2)+c cos2(A2)=3b2,a\,{\cos ^2}\left( {{C \over 2}} \right) + c\,{\cos ^2}\left( {{A \over 2}} \right) = {{3b} \over 2},acos2(2C)+ccos2(2A)=23b, then the sides a,ba, ba,b and ccc :OptionsAsatisfy a+b=ca+b=ca+b=cBare in A.PCare in G.PDare in H.PCheck AnswerHide SolutionSolutionIf a cos2(C2)+c cos2(A2)=3b2a\,{\cos ^2}\left( {{C \over 2}} \right) + c\,{\cos ^2}\left( {{A \over 2}} \right) = {{3b} \over 2}acos2(2C)+ccos2(2A)=23b a[cosC+1]+c[cosA+1]=3ba\left[ {\cos C + 1} \right] + c\left[ {\cos A + 1} \right] = 3ba[cosC+1]+c[cosA+1]=3b (a+c)+(acosC+ccos B)=3b\left( {a + c} \right) + \left( {a\cos C + c\cos \,B} \right) = 3b(a+c)+(acosC+ccosB)=3b a+c+b=3ba + c + b = 3ba+c+b=3b or a+c=2ba + c = 2ba+c=2b or a,b,ca,b,ca,b,c are in A.P.A.P.A.P.