Question

A solution of the equation tan^-1(1 + x) + tan^-1(1 - x) = `pi/2` is ______ 

पर्याय

• x = 1

• x = -1

• x = 0

• x = π

Answer 1

A solution of the equation tan^-1(1 + x) + tan^-1(1 - x) = `pi/2` is x = 0.

Explanation:

tan^-1(1 + x) + tan^-1(1 - x) = `pi/2`

⇒ `tan^-1(1 + x) = pi/2 - tan^-1(1 - x)`

⇒ `tan^-1(1 + x) = cot^-1(1 - x)`

⇒ `tan^-1(1 + x) = tan^-1(1/(1 - x))`

⇒ `1 + x = 1/(1 - x) ⇒ 1 - x^2 = 1 ⇒ x = 0`