Question

The value of 2 `cot^-1  1/2 - cot^-1  4/3` is ______ 

Options

• `-pi/8`

• `(3pi)/2`

• `pi/4`

• `pi/2`

Answer 1

The value of 2 `cot^-1  1/2 - cot^-1  4/3` is `underline(pi/2)`.

Explanation:

2 `cot^-1(1/2) - cot^-1(4/3)`

= `2tan^-1(2) - cot^-1 (4/3)` ..................[∵ `cot^-1(x) = tan^-1 (1/x)`, if x > 0]

= `pi + tan^-1(4/(-3)) - cot^-1 (4/3)` ......`[∵ 2tan^-1 (x) = pi + tan^-1((2x)/(1 - x^2)), "If"  x > 1]`

= `pi - tan^-1(4/3) - cot^-1(4/3)`

= `pi - [tan^-1 (4/3) + cot^-1(4/3)]`

= `pi - pi/2`

= `pi/2`