हिंदी

Evaluate the Following: `Cot^-1(Cot (9pi)/4)` - Mathematics

Advertisements
Advertisements

प्रश्न

Evaluate the following:

`cot^-1(cot  (9pi)/4)`

Advertisements

उत्तर

We know that

cot-1 (cot θ) = θ,   (0, π)

We have

`cot^-1(cot  (9pi)/4)=cot^-1[cot(2pi+pi/4)]`

`=cot^-1(cot  pi/4)`

`=pi/4`

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 4: Inverse Trigonometric Functions - Exercise 4.07 [पृष्ठ ४३]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 12
अध्याय 4 Inverse Trigonometric Functions
Exercise 4.07 | Q 6.3 | पृष्ठ ४३

वीडियो ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्न

Find the value of the following: `tan(1/2)[sin^(-1)((2x)/(1+x^2))+cos^(-1)((1-y^2)/(1+y^2))],|x| <1,y>0 and xy <1`


Solve the equation for x:sin1x+sin1(1x)=cos1x


If sin [cot−1 (x+1)] = cos(tan1x), then find x.


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


​Find the principal values of the following:

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


Evaluate the following:

`tan^-1(tan4)`


Evaluate the following:

`sec^-1(sec  pi/3)`


Evaluate the following:

`cot^-1(cot  (4pi)/3)`


Write the following in the simplest form:

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


Write the following in the simplest form:

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


Evaluate the following:

`cosec(cos^-1  3/5)`


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


`sin(sin^-1  1/5+cos^-1x)=1`


Prove the following result:

`tan^-1  1/4+tan^-1  2/9=sin^-1  1/sqrt5`


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


`sin^-1  63/65=sin^-1  5/13+cos^-1  3/5`


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


Prove that: `cos^-1  4/5+cos^-1  12/13=cos^-1  33/65`


Evaluate the following:

`sin(1/2cos^-1  4/5)`


`tan^-1  2/3=1/2tan^-1  12/5`


Solve the following equation for x:

`2tan^-1(sinx)=tan^-1(2sinx),x!=pi/2`


Write the range of tan−1 x.


Write the value of sin−1 \[\left( \cos\frac{\pi}{9} \right)\]


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


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


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


Write the value of \[\cos^{- 1} \left( \cos\frac{14\pi}{3} \right)\]


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


Write the value of  \[\tan^{- 1} \left( \frac{1}{x} \right)\]  for x < 0 in terms of `cot^-1x`


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


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


If  \[\cos^{- 1} \frac{x}{a} + \cos^{- 1} \frac{y}{b} = \alpha, then\frac{x^2}{a^2} - \frac{2xy}{ab}\cos \alpha + \frac{y^2}{b^2} = \]


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


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

 


If \[\tan^{- 1} \left( \frac{1}{1 + 1 . 2} \right) + \tan^{- 1} \left( \frac{1}{1 + 2 . 3} \right) + . . . + \tan^{- 1} \left( \frac{1}{1 + n . \left( n + 1 \right)} \right) = \tan^{- 1} \theta\] , then find the value of θ.


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


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


tanx is periodic with period ____________.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×