Question

In a triangle ABC, ∠C = 90°, then the value of `tan^-1 ("a"/("b + c")) + tan^-1("b"/("c + a"))` is ______.

Options

• `pi/3`

• `pi/4`

• `pi`

• `pi/2`

Answer 1

In a triangle ABC, ∠C = 90°, then the value of `tan^-1 ("a"/("b + c")) + tan^-1("b"/("c + a"))` is `underline(pi/4)`.

Explanation:

`tan^-1 ("a"/("b + c")) + tan^-1("b"/("c + a"))`

`= tan^-1 (("ac" + "bc" + "a"^2 + "b"^2)/("ac" + "bc" + "c"^2))   ...[because tan^-1 x + tan^-1 "y" = tan^-1 ((x + y)/(1 - xy))]`

`= tan^-1 (1)    ....[because "c"^2 = "a"^2 + "b"^2]`

`= pi/4`