English

Find the Value of Cos − 1 ( Cos 13 π 6 ) - Mathematics

Advertisements
Advertisements

Question

Find the value of \[\cos^{- 1} \left( \cos\frac{13\pi}{6} \right)\]

Advertisements

Solution

\[\cos^{- 1} \left( \cos\frac{13\pi}{6} \right) = \cos^{- 1} \left[ \cos\left( 2\pi + \frac{\pi}{6} \right) \right]\]
\[ = \cos^{- 1} \left[ \cos\left( \frac{\pi}{6} \right) \right]\]
\[ = \frac{\pi}{6}\]

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 59 | Page 119

RELATED QUESTIONS

If (tan1x)2 + (cot−1x)2 = 5π2/8, then find x.


​Find the principal values of the following:

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


`sin^-1(sin12)`


Evaluate the following:

`tan^-1(tan  (7pi)/6)`


Evaluate the following:

`tan^-1(tan  (9pi)/4)`


Evaluate the following:

`tan^-1(tan1)`


Evaluate the following:

`cot^-1(cot  pi/3)`


Evaluate the following:

`cot^-1(cot  (19pi)/6)`


Evaluate the following:

`cot^-1{cot  ((21pi)/4)}`


Write the following in the simplest form:

`tan^-1(x/(a+sqrt(a^2-x^2))),-a<x<a`


Evaluate the following:

`cosec(cos^-1  3/5)`


Prove the following result

`sin(cos^-1  3/5+sin^-1  5/13)=63/65`


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


Evaluate: `cos(sin^-1  3/5+sin^-1  5/13)`


Evaluate the following:

`sin(1/2cos^-1  4/5)`


Solve the following equation for x:

`3sin^-1  (2x)/(1+x^2)-4cos^-1  (1-x^2)/(1+x^2)+2tan^-1  (2x)/(1-x^2)=pi/3`


What is the value of cos−1 `(cos  (2x)/3)+sin^-1(sin  (2x)/3)?`


Write the value of sin−1

\[\left( \sin( -{600}°) \right)\].

 

 


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


Write the value of tan1\[\left\{ \tan\left( \frac{15\pi}{4} \right) \right\}\]


If \[\sin^{- 1} \left( \frac{1}{3} \right) + \cos^{- 1} x = \frac{\pi}{2},\] then find x.

 


Write the value of \[\tan\left( 2 \tan^{- 1} \frac{1}{5} \right)\]


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


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


If \[\cos\left( \sin^{- 1} \frac{2}{5} + \cos^{- 1} x \right) = 0\], find the value of x.

 

The value of tan \[\left\{ \cos^{- 1} \frac{1}{5\sqrt{2}} - \sin^{- 1} \frac{4}{\sqrt{17}} \right\}\] is

 


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


\[\text{ If }\cos^{- 1} \frac{x}{3} + \cos^{- 1} \frac{y}{2} = \frac{\theta}{2}, \text{ then }4 x^2 - 12xy \cos\frac{\theta}{2} + 9 y^2 =\]


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


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

 


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


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


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


Find the real solutions of the equation
`tan^-1 sqrt(x(x + 1)) + sin^-1 sqrt(x^2 + x + 1) = pi/2`


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×