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  • Considering only the principal values , if tan^-(1/2) , tan^(1/3) and tan^-1(k) are in A.P then k equals

Considering only the principal values , if tan^-(1/2) , tan^(1/3) and tan^-1(k) are in A.P then k equals

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Solution:      an^-1(1/2), tan^-1(1/3), tan^-1k

              2 an^-1(1/3)= an^-1(1/2)+ an^-1(k)

          Rightarrow     an^-1[2(1/3)/1-(1/3)^2]= an^-1[(1/2)+(k)/1-(1/2)(k)]

         Rightarrow          k=2/11 ans

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Deependra Verma

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