हिंदी

Evaluate the Following: `Tan^-1(Tan12)` - Mathematics

Advertisements
Advertisements

प्रश्न

Evaluate the following:

`tan^-1(tan12)`

उत्तर

We know that

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

We have 

`tan^-1(tan12)=tan^-1[tan(-4pi+12)]`

= 12 - 4π

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 4: Inverse Trigonometric Functions - Exercise 4.07 [पृष्ठ ४२]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 12
अध्याय 4 Inverse Trigonometric Functions
Exercise 4.07 | Q 3.8 | पृष्ठ ४२

वीडियो ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्न

Solve for x:

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


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


Prove that

`tan^(-1) [(sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x))]=pi/4-1/2 cos^(-1)x,-1/sqrt2<=x<=1`


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


`sin^-1(sin  (17pi)/8)`


Evaluate the following:

`cos^-1{cos  (5pi)/4}`


Evaluate the following:

`tan^-1(tan4)`


Evaluate the following:

`cosec^-1(cosec  (13pi)/6)`


Write the following in the simplest form:

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


Write the following in the simplest form:

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


Write the following in the simplest form:

`sin^-1{(sqrt(1+x)+sqrt(1-x))/2},0<x<1`


Evaluate the following:

`sin(sin^-1  7/25)`

 


Evaluate the following:

`tan(cos^-1  8/17)`


Evaluate:

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


Find the value of `tan^-1  (x/y)-tan^-1((x-y)/(x+y))`


Evaluate the following:

`tan{2tan^-1  1/5-pi/4}`


Evaluate the following:

`sin(1/2cos^-1  4/5)`


Evaluate the following:

`sin(2tan^-1  2/3)+cos(tan^-1sqrt3)`


Prove that

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


Find the value of the following:

`tan^-1{2cos(2sin^-1  1/2)}`


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`


Prove that `2tan^-1(sqrt((a-b)/(a+b))tan  theta/2)=cos^-1((a costheta+b)/(a+b costheta))`


If x > 1, then write the value of sin−1 `((2x)/(1+x^2))` in terms of tan−1 x.


Evaluate sin

\[\left( \frac{1}{2} \cos^{- 1} \frac{4}{5} \right)\]


Write the value of cos\[\left( \frac{1}{2} \cos^{- 1} \frac{3}{5} \right)\]


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


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


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


Write the principal value of `sin^-1(-1/2)`


The set of values of `\text(cosec)^-1(sqrt3/2)`


Wnte the value of\[\cos\left( \frac{\tan^{- 1} x + \cot^{- 1} x}{3} \right), \text{ when } x = - \frac{1}{\sqrt{3}}\]


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


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

 


In a ∆ ABC, if C is a right angle, then
\[\tan^{- 1} \left( \frac{a}{b + c} \right) + \tan^{- 1} \left( \frac{b}{c + a} \right) =\]

 

 


Prove that : \[\cot^{- 1} \frac{\sqrt{1 + \sin x} + \sqrt{1 - \sin x}}{\sqrt{1 + \sin x} - \sqrt{1 - \sin x}} = \frac{x}{2}, 0 < x < \frac{\pi}{2}\] .


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


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×