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  • If sin^-1 x + sin ^-1 y +sin^-1 z =3pi/2 then value of Sigma (x^101 + y^101 ) (x^505 + y ^ 505 ) /(x^303 + y^303 ) (x^606 +y^606)

If sin^-1 x + sin ^-1 y +sin^-1 z =3pi/2 then value of Sigma (x^101 + y^101 ) (x^505 + y ^ 505 ) /(x^303 + y^303 ) (x^606 +y^606)

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Solution:    We have ,

                 sin^-1x+sin^-1 y+sin^-1z=frac3pi2

                    It is possible only  When

             Rightarrow    sin^-1x=sin^-1y=sin^-1z=fracpi2.

            Rightarrow           x=y=z=1.

           Now ,  sum frac(x^101+y^101)(x^505+y^505)(x^303+y^303)(x^606+y^606)=sum frac(1+1)(1+1)(1+1)(1+1)=sum 1=(1+1+1)=3.          

               

             

        

Posted by

Deependra Verma

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