Question

If x > 0, y > 0, xy > 1, then tan^-1x + tan^-1y = _____________________.

Answer 1

We know

${\tan }^{-1}x+{\tan }^{-1}y=\mathrm{\pi }+{\tan }^{-1}\left(\frac{x+y}{1-xy}\right)$, if x > 0, y > 0 and xy > 1

If x > 0, y > 0, xy > 1, then tan⁻¹x + tan⁻¹y = $\underline{\mathrm{\pi }+{\tan }^{-1}\left(\frac{x+y}{1-xy}\right)}$.