Question

How do you prove `cot^-1(x)=pi/2-tan^-1(x)`?

Answer 1

Kindly see the solution for the answer

Explanation:

The solution

Let `alpha` be the angle with tangent`=x`
Let `beta=pi/2-alpha` be the angle with cotangent `=x`

Then `alpha+beta=pi/2`

`cot^-1 x=pi/2-tan^-1 x`

`cot^-1 x=pi/2-tan^-1 x`

`cot^-1 x=pi/2-(pi/2-cot^-1 x)`

`cot^-1 x=pi/2-pi/2+cot^-1 x`

`cot^-1 x=cot^-1 x`

God bless....I hope the explanation is useful.