Question

if cosec^2 theta =4xy/(x+y)^2 then find relation between x and y

Answer 1

x = y

cosec^2x = 4xy(x+y)^2

4xy = (x+y)^2 - (x-y)^2

So , Our Equation  can be written as
=> cosec^2x = ((x+y)^2 - (x-y)^2)/(x+y)^2
=>cosec^2x = 1 - (x-y)^2/(x+y)^2

((x-y)/(x+y))^2 is always greater than or equal to 0.

=>cosec^2x = 1 - (non-negative quantity)
 
But cosec^2x is always greater than or equal to 1.

non-negative quantity should be 0.

So, ((x-y)/(x+y))^2 = 0
=> x-y = 0
=> x = y.

So, this is only possible when x = y.