Show that the equation `sec^2 theta=(4xy)/(x+y)^2` is only possible when x=y

Prove that the relation sin^(2)theta = (x+y)^(2)/4xy is not 4xy possible for any real theta where x in R , y in R such that |x | ne ly| .

The equation sin^(2)theta=(x^(2)+y^(2))/(2xy),x,y!=0 is possible if

sec^(2)theta = 4xy/(x+y)^(2) is true if and only if

cos ec^(2)theta=(4xy)/((x+y)^(2)) is true if and only if

Show that sin^(2)theta=(x^(2)+y^(2))/(2xy) is possible for real value of x and y only when x=y!=0