Fill in the blanks:The value of cot–1(–x) for all x ϵ R in ter

1.	Fill in the blanks:The value of cot–1(–x) for all x ϵ R in terms of cot–1 x is _______.
Answer» 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

Fill in the blanks:The value of cot–1(–x) for all x ϵ R in terms of cot–1 x is _______.

Answer»

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