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

Find the value of (( x -y )^3 + ( y - z )^3 + ( z - x )^3 )/ (9 ( x - y )( y - z ) ( z - x )) 1 . 0 2 . 1/9 3 . 1/3 4. 1

Find the value of ( (x^-2 times y^-4 )/ ( x^-3 times y^-1) ÷ y^-2/x^-1 )

If y=(sin^(-1)x cos^(-1)((x^2)/2))/(1+x^2) then find the value of y(1/2) + y(1/sqrt2) + y(-1/2) + y(-1/sqrt2)

If x gt y gt z gt 0 , then find the value of "cot"^(-1) (xy + 1)/(x - y) + "cot"^(-1)(yz + 1)/(y - z) + "cot"^(-1)(zx + 1)/(z - x)

Find the value of |{:(1, " "1, " "1), (1, 1+x, " "1), (1, " "1, 1+y):}|.

If 2^(x)=3^(y)=6^(-z) find the value of ((1)/(x)+(1)/(y)+(1)/(z))

If x=(a-b)/(a+b), y=(b-c)/(b+c) and z=(c-a)/(c+a) , find the value of ((1+x)(1+y)(1+z))/((1-x)(1-y)(1-z))

If x,y in R^(+) such that x + y = 8, then find the minimum value of (1 + (1)/(x)) (1 + (1)/(y))

If sec^(-1) x = cosec^(-1) y , then find the value of cos^(-1) . 1/x + cos ^(-1) . 1/y .

Suppose x;y;z>0 and are not equal to 1 and log x+log y+log z=0. Find the value of x(1)/(log y)+(1)/(log z)xx y^((1)/(log z)+(1)/(log x))xx(1)/(log x)+(1)/(log y) (base 10)