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If tan^(2) {pi(x+y)}+cot^(2) {pi (x+y)}=...

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.

Text Solution

Verified by Experts

The correct Answer is:
`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`.
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