The value of cot^–1(–x) for all x ϵ R in terms of cot^–1 x is _______.

Question

Fill in the blanks:

The value of cot^–1(–x) for all x ϵ R in terms of cot^–1 x is _______.

Answer 1

The value of cot^–1(–x) for all x ϵ R in terms of cot^–1 x is

π – cot^-1 x.

Let cot^–1(–x) = A

⇒ cot A = -x

⇒ -cot A = x

⇒ cot (π – A) = x

⇒ (π – A) = cot^-1 x

⇒ A = π – cot^-1 x

So, cot^–1(–x) = π – cot^-1 x