Question

If `tan^(−1)(a/x) + tan^(−1)(b/x) = π/2,` then x is equal to ______.

Options

• `sqrt(ab)`

• `sqrt(2ab)`

• 2ab

• ab

Answer 1

If `tan^(−1)(a/x) + tan^(−1)(b/x) = π/2,` then x is equal to `bbunderline sqrt(ab)`.

Explanation:

Let `tan^(−1) (a/x) + tan^(−1)(b/x) = π/2`

⇒ `tan^(−1)((a/x + b/x)/(1 − (ab)/x^2))`

⇒ `x/2 = (a/x + b/x)/(1 − (ab)/x^2)`

⇒ tan `π/2`

⇒ `1 − (ab)/x^2 = 0`

x = `sqrt(ab)`