English

Evaluate the Following: `Cot^-1{Cot ((21pi)/4)}` - Mathematics

Advertisements
Advertisements

Question

Evaluate the following:

`cot^-1{cot  ((21pi)/4)}`

Solution

We know that

cot-1 (cot θ) = θ,   (0, π)

We have

`cot^-1{cot  (21pi)/4}=cot^-1[cot(5pi+pi/4)]`

`=cot^-1(cot  pi/4)`

`=pi/4`

 

shaalaa.com
  Is there an error in this question or solution?
Chapter 4: Inverse Trigonometric Functions - Exercise 4.07 [Page 43]

APPEARS IN

RD Sharma Mathematics [English] Class 12
Chapter 4 Inverse Trigonometric Functions
Exercise 4.07 | Q 6.6 | Page 43

RELATED QUESTIONS

 

Prove that :

`2 tan^-1 (sqrt((a-b)/(a+b))tan(x/2))=cos^-1 ((a cos x+b)/(a+b cosx))`

 

If a line makes angles 90° and 60° respectively with the positive directions of x and y axes, find the angle which it makes with the positive direction of z-axis.


​Find the principal values of the following:

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


​Find the principal values of the following:

`cos^-1(sin   (4pi)/3)`


​Find the principal values of the following:

`cos^-1(tan  (3pi)/4)`


`sin^-1(sin  (5pi)/6)`


Evaluate the following:

`tan^-1(tan1)`


Evaluate the following:

`tan^-1(tan4)`


Evaluate the following:

`sec^-1(sec  pi/3)`


Evaluate the following:

`sec^-1(sec  (25pi)/6)`


Evaluate the following:

`cosec^-1{cosec  (-(9pi)/4)}`


Write the following in the simplest form:

`tan^-1{sqrt(1+x^2)-x},x in R `


Evaluate:

`sec{cot^-1(-5/12)}`


Evaluate: 

`cot(sin^-1  3/4+sec^-1  4/3)`


If `cos^-1x + cos^-1y =pi/4,`  find the value of `sin^-1x+sin^-1y`


Solve the following equation for x:

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


Solve the following:

`cos^-1x+sin^-1  x/2=π/6`


If `cos^-1  x/2+cos^-1  y/3=alpha,` then prove that  `9x^2-12xy cosa+4y^2=36sin^2a.`


Solve the equation `cos^-1  a/x-cos^-1  b/x=cos^-1  1/b-cos^-1  1/a`


Evaluate the following:

`tan  1/2(cos^-1  sqrt5/3)`


`tan^-1  1/7+2tan^-1  1/3=pi/4`


`sin^-1  4/5+2tan^-1  1/3=pi/2`


Write the value of

\[\cos^{- 1} \left( \frac{1}{2} \right) + 2 \sin^{- 1} \left( \frac{1}{2} \right)\].


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


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


If x < 0, y < 0 such that xy = 1, then write the value of tan1 x + tan−1 y.


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


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


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


If sin−1 − cos−1 x = `pi/6` , then x = 


If x < 0, y < 0 such that xy = 1, then tan−1 x + tan−1 y equals

 


Let f (x) = `e^(cos^-1){sin(x+pi/3}.`
Then, f (8π/9) = 


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


If \[3\sin^{- 1} \left( \frac{2x}{1 + x^2} \right) - 4 \cos^{- 1} \left( \frac{1 - x^2}{1 + x^2} \right) + 2 \tan^{- 1} \left( \frac{2x}{1 - x^2} \right) = \frac{\pi}{3}\] is equal to

 


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

 


Find the domain of `sec^(-1)(3x-1)`.


Find the simplified form of `cos^-1 (3/5 cosx + 4/5 sin x)`, where x ∈ `[(-3pi)/4, pi/4]`


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×