English

Write the Value of Cot − 1 ( − X ) for All X ∈ R in Terms of Cot − 1 ( X ) - Mathematics

Advertisements
Advertisements

Question

Write the value of  `cot^-1(-x)`  for all `x in R` in terms of `cot^-1(x)`

Solution

We know that 
\[\cot^{- 1} \left( - x \right) = \pi - \cot^{- 1} \left( x \right)\] Therefore, the value of  \[\cot^{- 1} \left( - x \right)\]  for all `x in R`   in terms of `cot^-1(x)`   is `pi-cot^-1(x)`

shaalaa.com
  Is there an error in this question or solution?
Chapter 4: Inverse Trigonometric Functions - Exercise 4.15 [Page 119]

APPEARS IN

RD Sharma Mathematics [English] Class 12
Chapter 4 Inverse Trigonometric Functions
Exercise 4.15 | Q 54 | Page 119

RELATED QUESTIONS

Solve for x:

`2tan^(-1)(cosx)=tan^(-1)(2"cosec" x)`


Find the domain of  `f(x) =2cos^-1 2x+sin^-1x.`


​Find the principal values of the following:

`cos^-1(-1/sqrt2)`


Evaluate the following:

`tan^-1(tan2)`


Evaluate the following:

`tan^-1(tan4)`


Evaluate the following:

`tan^-1(tan12)`


Evaluate the following:

`sec^-1{sec  (-(7pi)/3)}`


Evaluate the following:

`\text(cosec)^-1(\text{cosec}  pi/4)`


Evaluate:

`tan{cos^-1(-7/25)}`


`tan^-1x+2cot^-1x=(2x)/3`


Solve the following equation for x:

`tan^-1((x-2)/(x-4))+tan^-1((x+2)/(x+4))=pi/4`


Evaluate the following:

`tan  1/2(cos^-1  sqrt5/3)`


`2sin^-1  3/5-tan^-1  17/31=pi/4`


`2tan^-1  3/4-tan^-1  17/31=pi/4`


`4tan^-1  1/5-tan^-1  1/239=pi/4`


Prove that

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


Solve the following equation for x:

`cos^-1((x^2-1)/(x^2+1))+1/2tan^-1((2x)/(1-x^2))=(2x)/3`


Solve the following equation for x:

`tan^-1((x-2)/(x-1))+tan^-1((x+2)/(x+1))=pi/4`


If −1 < x < 0, then write the value of `sin^-1((2x)/(1+x^2))+cos^-1((1-x^2)/(1+x^2))`


Write the value of cos−1 (cos 1540°).


Write the value of cos−1 \[\left( \tan\frac{3\pi}{4} \right)\]


Write the value ofWrite the value of \[2 \sin^{- 1} \frac{1}{2} + \cos^{- 1} \left( - \frac{1}{2} \right)\]


Write the value of \[\tan^{- 1} \frac{a}{b} - \tan^{- 1} \left( \frac{a - b}{a + b} \right)\]


Show that \[\sin^{- 1} (2x\sqrt{1 - x^2}) = 2 \sin^{- 1} x\]


If 4 sin−1 x + cos−1 x = π, then what is the value of x?


Write the value of \[\tan^{- 1} \left\{ 2\sin\left( 2 \cos^{- 1} \frac{\sqrt{3}}{2} \right) \right\}\]


Write the value of \[\cos\left( \sin^{- 1} x + \cos^{- 1} x \right), \left| x \right| \leq 1\]


Find the value of \[\tan^{- 1} \left( \tan\frac{9\pi}{8} \right)\]


2 tan−1 {cosec (tan−1 x) − tan (cot1 x)} is equal to


The number of solutions of the equation \[\tan^{- 1} 2x + \tan^{- 1} 3x = \frac{\pi}{4}\] is

 


If \[\cos^{- 1} \frac{x}{2} + \cos^{- 1} \frac{y}{3} = \theta,\]  then 9x2 − 12xy cos θ + 4y2 is equal to


sin \[\left\{ 2 \cos^{- 1} \left( \frac{- 3}{5} \right) \right\}\]  is equal to

 


If > 1, then \[2 \tan^{- 1} x + \sin^{- 1} \left( \frac{2x}{1 + x^2} \right)\] is equal to

 


The domain of  \[\cos^{- 1} \left( x^2 - 4 \right)\] is

 


Prove that : \[\tan^{- 1} \left( \frac{\sqrt{1 + x^2} + \sqrt{1 - x^2}}{\sqrt{1 + x^2} - \sqrt{1 - x^2}} \right) = \frac{\pi}{4} + \frac{1}{2} \cos^{- 1} x^2 ;  1 < x < 1\].


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×