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  • If tan^-1 x - cot^-1 x=tan^-1 (1/square root 3) , Find the value of x .

If tan^-1 x - cot^-1 x=tan^-1 (1/square root 3) , Find the value of x .

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Solution:    We have ,

                  an^-1x-cot^-1x= an-1(1/sqrt3)

             Rightarrow    an^-1x-cot^-1x=pi/6         ..........(1)

     We know that ,  an^-1x+cot^-1x=pi/2        ..........(2)

        Adding (1) and (2)  , We obtain

     2 an^-1x=2pi/3Rightarrow an^-1 x=pi/3Rightarrow x=sqrt3

           Rightarrow      

Posted by

Deependra Verma

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