English

Evaluate the Following: `Tan^-1(Tan1)` - Mathematics

Advertisements
Advertisements

Question

Evaluate the following:

`tan^-1(tan1)`

Solution

We know that

`tan^-1(tantheta)=theta,   -pi/2<theta<pi/2`

We have 

`tan^-1(tan1)=1`

shaalaa.com
  Is there an error in this question or solution?
Chapter 4: Inverse Trigonometric Functions - Exercise 4.07 [Page 42]

APPEARS IN

RD Sharma Mathematics [English] Class 12
Chapter 4 Inverse Trigonometric Functions
Exercise 4.07 | Q 3.5 | Page 42

RELATED QUESTIONS

 

If `tan^(-1)((x-2)/(x-4)) +tan^(-1)((x+2)/(x+4))=pi/4` ,find the value of x

 

​Find the principal values of the following:

`cos^-1(tan  (3pi)/4)`


`sin^-1(sin  (13pi)/7)`


`sin^-1(sin4)`


`sin^-1(sin2)`


Evaluate the following:

`cos^-1(cos12)`


Evaluate the following:

`tan^-1(tan  (6pi)/7)`


Evaluate the following:

`sec^-1(sec  (7pi)/3)`


Evaluate the following:

`cot^-1(cot  pi/3)`


Evaluate the following:

`cot^-1(cot  (4pi)/3)`


Evaluate the following:

`cot^-1(cot  (9pi)/4)`


Evaluate the following:

`cot^-1(cot  (19pi)/6)`


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)`


Evaluate the following:

`cos(tan^-1  24/7)`


Evaluate:

`cot{sec^-1(-13/5)}`


Evaluate: `sin{cos^-1(-3/5)+cot^-1(-5/12)}`


Evaluate:

`sin(tan^-1x+tan^-1  1/x)` for x < 0


If `sin^-1x+sin^-1y=pi/3`  and  `cos^-1x-cos^-1y=pi/6`,  find the values of x and y.


Solve the following equation for x:

 cot−1x − cot−1(x + 2) =`pi/12`, > 0


Solve the following equation for x:

tan−1(x + 2) + tan−1(x − 2) = tan−1 `(8/79)`, x > 0


Solve the following equation for x:

`tan^-1(2+x)+tan^-1(2-x)=tan^-1  2/3, where  x< -sqrt3 or, x>sqrt3`


`tan^-1  1/4+tan^-1  2/9=1/2cos^-1  3/2=1/2sin^-1(4/5)`


Prove that

`sin{tan^-1  (1-x^2)/(2x)+cos^-1  (1-x^2)/(2x)}=1`


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`


Write the value of tan1x + tan−1 `(1/x)`for x > 0.


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


Write the value of cos−1 \[\left( \cos\frac{5\pi}{4} \right)\]


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


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


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


The number of real solutions of the equation \[\sqrt{1 + \cos 2x} = \sqrt{2} \sin^{- 1} (\sin x), - \pi \leq x \leq \pi\]


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


It \[\tan^{- 1} \frac{x + 1}{x - 1} + \tan^{- 1} \frac{x - 1}{x} = \tan^{- 1}\]   (−7), then the value of x is

 


\[\cot\left( \frac{\pi}{4} - 2 \cot^{- 1} 3 \right) =\] 

 


Find : \[\int\frac{2 \cos x}{\left( 1 - \sin x \right) \left( 1 + \sin^2 x \right)}dx\] .


Solve for x : {xcos(cot-1 x) + sin(cot-1 x)}= `51/50`


The value of tan `("cos"^-1  4/5 + "tan"^-1  2/3) =`


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×