If `x<0,\ y<0` such that `x y=1` , then write the value of `tan^(-1)x+tan^(-1)y` .

Explanation

We are given that, `xy = 1, x < 0` and `y < 0`

We need to find the value of `tan^(-1) x + tan^(-1) y`.

Using the property of inverse trigonometry, `tan^(-1) x + tan^(-1) y = tan^(-1) frac{( x + y)}{( 1 − 1 )}

` tan^(-1)=frac{ ( x + y)}{ 0 )}.

And since `(x + y)` = negative value = integer = -a (say).

`tan^(-1)frac{-a}{0}`

`tab^(-1)x+tan^(-1)y=tan^(-1)-oo`

`tan^(-1)x+tan^(-1)y=frac{-pi}{2}`