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  • If cos^-1 6x/1+9x^2 =-pi/2 +2 tan^-1 3x , then find the values of x .

If cos^-1 6x/1+9x^2 =-pi/2 +2 tan^-1 3x , then find the values of x .

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Solution:  We have ,

                   cos^-1frac6x1+9x^2=-fracpi2+2 an^-13x

            Rightarrow       fracpi2-sin^-1frac6x1+9x^2=-fracpi2+2 an^-13x

          Rightarrow      pi-2 an^-13x=sin^-1frac2(3x)1+(3x)^2

           We know that ,       sin^-1frac2x1+x^2=pi-2 an^-1x hspace0.5cmif hspace0.2cmx> 1

       Therefore                3x> 1Rightarrow x> frac13     ,   Thus xin(frac13,infty ).   

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Deependra Verma

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