Find the value of `1/(1+x)+2/(1+x^2)+2^2/(1+x^4)+ . . . + 2^100/(1+x^200)`

Find the value of x if 2^x -2^(x-1) = 4

Find the value of ( x - 1/x )( x + 1/x ) ( x^2 + 1/x^2 ) =

If (x - 1/x) = 4 , find the value of (i) (x^(2) - 1/(x^(2))) , (ii) (x^(4) + 1/(x^(4))).

If x + (1)/(x) = 5 find the values of (i) x^(2) + (1)/(x^(2)) and (ii) x^(4) + (1)/(x^(4))

Find the value of ( 1/x + 1/y ) ( 1/x - 1/y ) ( 1/x^2 + 1/y^2 )

If x-(1)/(x)=3, find the values of x^(2)+(1)/(x^(2)) and x^(4)+(1)/(x^(4))

If x in (0, 1) , then find the value of tan^(-1) ((1 -x^(2))/(2x)) + cos^(-1) ((1 -x^(2))/(1 + x^(2)))

If x+(1)/(x)=sqrt(5), find the values of x^(2)+(1)/(x^(2)) and x^(4)+(1)/(x^(4))

Find the value of : ( x^(1/2 ) + x^(-1/2 ) ) times ( x^(1/4 ) + x^(-1/4 ) ) times ( x^(1/8 ) + x^(-1/8 ) ) times ( x^(1/8 ) - x^(-1/8 ) ) ( a ) x + 1/x ( b ) ( x^2 -1 )/x