Question

If `tan^(2) {pi(x+y)}+cot^(2) {pi (x+y)}=1+sqrt((2x)/(1+x^(2)))` where `x, y in R`, then find the least possible value of y.

Answer 1

Correct Answer - `1//4`
`LHS ge 2, RHS le 2`
Equality is possible
The for `RHS, x=1`
For `LHS, tan^(2) pi (1+y)=1`
`:. tan^(2) pi y=1`
Least value of y ia `1/4`.