Find the set of values of x for which the equation cos^-1 x+ cos^-1( x/2 +(1/2) square root 3-3x^2 ) holds good

Answers (1)

Solution:   

                cos^-1 x+cos^-1(fracx2+frac12sqrt(3-3x^2))=fracpi3.

       Rightarrow           cos^-1 x+cos^-1(frac12 x+fracsqrt32sqrt(1-x^2))=fracpi3.    

      Rightarrow             cos^-1x+cos^-1frac12 -cos^-1x=fracpi3.

        ecause         frac12leq xleq 1    so ,   cos^-1frac12-cos^-1x> 0

        Thus           xin[frac12,1].     

                

                        

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