" Show that: ":(x^(-1)+y^(-1))/(x^(-1))+(x^(-1)-y^(-1))/(x^(-1))=(x^(2)+y^(2))/(xy)

Prove that ((x^(-1)+y^(-1)))/(x^(-1))+((x^(-1)+y^(-1)))/(y^(-1))=(x+y)^2/(xy)

If the points (x_(1),y_(1)),(x_(2),y_(2)), and (x_(3),y_(3)) are collinear show that (y_(2)-y_(3))/(x_(2)x_(3))+(y_(3)-y_(1))/(x_(3)x_(1))+(y_(1)-y_(2))/(x_(1)x_(2))=0

If xy+yz+zx=1 show that (x)/(1-x^(2))+(y)/(1-y^(2))+(z)/(1-z^(2))=(4xyz)/((1-x^(2))(1-y^(2))(1-z^(2)))

If xy + yz + zx = 1 , show that x/(1-x^(2)) +y/(1-y^(2)) + z/(1-z^(2))= (4xyz)/((1-x^(2))(1-y^(2)) (1-z^(2)))

If xy + yz + zx = 1 , show that x/(1-x^(2)) +y/(1-y^(2)) + z/(1-z^(2))= 4xyz/((1-x^(2))(1-y^(2)) (1-z^(2)))

If xy=1+a^(2) then show that tan^(-1)((1)/(a+x))+tan^(-1)((1)/(a+y))=tan^(-1)((1)/(a)),x+y+2a!=0

The factors of x^(3)-1+y^(3)+3xy are (a) (x-1+y)(x^(2)+1+y^(2)+x+y-xy)( b) (x+y+1)(x^(2)+y^(2)+1-xy-x-y)( c) (x-1+y)(x^(2)-1-y^(2)+x+y+xy)(d)3(x+y-1)(x^(2)+y^(2)-1)

If xy=1 + a^(2) then show that tan^(-1) ""(1)/(a+x)+tan ^(-1) ""(1)/(a+y)=tan ^(-1)""(1)/(a) , x+y+2a ne 0

Prove that tan^(-1)(1/(x+y))+tan^(-1)(y/(x^2+xy+1) )= cot^(-1)x .