If `x=1+(y)/(2)+((y)/(2))^(2)+((y)/(2))^(3)+……" where "|y|lt2`, what is 1y equal to ?

If (x)/(2)+(y)/(3)=4 "and" (2)/(x)+(3)/(y)=1 then what is x+y equal to ?

If (3)/(x+y)+(2)/(x-y)=2 and (9)/(x+y)-(4)/(x-y)=1 then what is (x)/(y) equal to ?

If (dy)/(dx)=(2^(x+y)-2^(x))/(2^(y)),y(0)=1 then y(1) is equal to

Prove that tan{1/2sin^(-1)((2x)/(1+x^(2)))+1/2cos^(-1)((1-y^(2))/(1+y^(2)))}=(x+y)/(1-xy) , where |x| lt 1,y gt 0 and xy lt 1 .

If y=(1)/(2)sin^(-1)((2xy)/(x^(2)+y^(2))) and y lt x then Lt_(y to 0)=

if y = x + x^(2) + x^(3) + …oo, where |x| lt 1, then for |y| lt 1, (dx)/(dy) is equal to

If sinx=(1)/(sqrt5).siny=(1)/(sqrt(10)) , where 0 lt x lt (pi)/(2),0 lt y lt (pi)/(2) , then what is (x+y) equal to?

int(1)/(3x^(2)y^(2)) where y is constant

If x/2 + y/3 = 4 and 2/x + 3/y = 1, then what is x + y equal to ?