Simplify -11-x2-1 for x-1

Let y= cot^ 11/√(x^2 1), x lt; 1 Put x= sec θ⇒θ = sec^ 1 x. Then sec θ lt; 1 ⇒π/2 lt; θ lt; π ∴ y= cot^ 11/√(sec^2θ 1)= cot^ 1 ( 1/|tan θ| ) ⇒ y= co ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Standard Limits to Remove Indeterminate Form

Simplify -11/...

Question

Simplify $c o t^{- 1} \frac{1}{\sqrt{x^{2} - 1}}$ for x<-1.

Open in App

Solution

Let $y = c o t^{- 1} \frac{1}{\sqrt{x^{2} - 1}}, x < - 1$
Put $x = s e c θ \Rightarrow θ = s e c^{- 1} x$ . Then $s e c θ < - 1 \Rightarrow \frac{π}{2} < θ < π$
$∴ y = c o t^{- 1} \frac{1}{\sqrt{s e c^{2} θ - 1}} = c o t^{- 1} (\frac{1}{| t a n θ |}) \Rightarrow y = c o t^{- 1} (\frac{1}{- t a n θ}) = c o t^{- 1} (- c o t θ)$
$\Rightarrow y = c o t^{- 1} (c o t (π - θ)) = π - θ$ $∴ y = π - s e c^{- 1} x$ .

Suggest Corrections

Similar questions

Q. Simplify

{cot}^{- 1} \frac{1}{\sqrt{x^{2} - 1}}

for

x < - 1

Q. Simplify :

{cot}^{- 1} [\sqrt{1 + x^{2}} - x]

Q. Simplify:

{tan}^{- 1} (\frac{1 - x^{2}}{1 + x^{2}})

Q. For all

x \neq 0

, simplify

\frac{5}{(\frac{1}{x^{2}})}

Q. Simplify:

{(x + \frac{1}{x})}^{2} - {(x - \frac{1}{x})}^{2}

Join BYJU'S Learning Program

Simplify cot−11√x2−1 for x<-1.

Let y=cot−11√x2−1, x<−1 Put x=sec θ⇒θ=sec−1x. Then sec θ<−1⇒π2<θ<π ∴y=cot−11√sec2θ−1=cot−1(1|tanθ|)⇒y=cot−1(1−tan θ)=cot−1(−cot θ) ⇒y=cot−1(cot(π−θ))=π−θ ∴y=π−sec−1x.

Simplify $c o t^{- 1} \frac{1}{\sqrt{x^{2} - 1}}$ for x<-1.