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If the angles A , B and C of a triangle are in A.P and if a, b and c denote the lengths of the sides opposite to A, B and C respectively , then the value of [ (a/c) sin 2C +(c/a) sin 2A ] is

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Solution:    A  , B and C are in A.P

                 Rightarrow     angle A=30^circ,angle B=60^circ  and   angle C=90^circ

                By sin Formula  ,      

                 fracasin A=fracbsin B=fraccsin C,

          or        fracafrac12=fracbfracsqrt32=fracc1=lambda

          	herefore          [fracacsin 2C+fraccasin 2A]=0+2sin 60^circ=sqrt3.

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Deependra Verma

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