Question

The value of `tan^-1 (1/3) + tan^-1 (1/5) + tan^-1 (1/7) + tan^-1 (1/8)`is ______.

Options

• `pi/6`

• `pi/3`

• `pi/4`

• `pi/12`

Answer 1

The value of `tan^-1 (1/3) + tan^-1 (1/5) + tan^-1 (1/7) + tan^-1 (1/8)` is `underline(pi/4)`.

Explanation:

We have,

`tan^-1 (1/3) + tan^-1 (1/5) + tan^-1 (1/7) + tan^-1 (1/8)`

`= tan^-1 ((1/3 + 1/5)/(1 - 1/3 xx 1/5)) + tan^-1 ((1/7 + 1/8)/(1 - 1/7 xx 1/8))`

`= tan^-1 (8/14) + tan^-1 (15/55)`

`= tan^-1 (4/7) + tan^-1 (3/11)`

`= tan^-1 ((4/7 + 3/11)/(1 - 4/7 xx 3/11))`

`= tan^-1 (65/65)`

`= tan^-1 = pi/4`