Question

If ΔABC is a right angled at C, then tan A + tan B is equal to ______.

Options

• `b^2/(ac)`

• a + b

• `a^2/(bc)`

• `c^2/(ab)`

Answer 1

If ΔABC is a right angled at C, then tan A + tan B is equal to `underlinebb(c^2/(ab))`.

Explanation:

Clearly, tan A = `a/b`, tan B = `b/a`

Now, tan A + tan B = `(a^2 + b^2)/(ab)`

∵ a² + b² = c²

∴ tan A + tan B = `c^2/(ab)`