What is the value of tan-1 x + cot-1 x ?

Question

What is the value of tan-1 x + cot-1 x ? (A) (π/2) textfor x > 0 textand - (π/2) textfor x < 0  (B) (π/2) textfor textall x  (C)  - (π/2) textfor textall x  (D) (π/2) textfor textintegral x

Tardigrade Admin · Accepted Answer

Let tan-1 x = p so, tan p = x tan p = cot ((π/2) - p ) ⇒ x = cot ((π/2) - p ) ⇒ cot-1 x = (π/2) - p So, tan-1 x + cot-1 x = p + (π/2) - p = (π/2) , ∀ x ∈ R

Q. What is the value of $tan^{- 1} x + cot^{- 1} x$ ?

$\frac{π}{2} for x > 0 and - \frac{π}{2} for x < 0$

$\frac{π}{2} for all x$

$- \frac{π}{2} for all x$

$\frac{π}{2} for integral x$

Let $tan^{- 1} x = p$ so, $tan p = x$
$tan p = cot (\frac{π}{2} - p)$
$\Rightarrow x = cot (\frac{π}{2} - p) \Rightarrow cot^{- 1} x = \frac{π}{2} - p$
So, $tan^{- 1} x + cot^{- 1} x = p + \frac{π}{2} - p$
$= \frac{π}{2}, \forall x \in R$

Q. What is the value of tan−1x+cot−1x ?

2π​forx>0and−2π​forx<0

2π​forallx

−2π​forallx

2π​forintegralx