हिंदी

Evaluate the Following: `Cos^-1{Cos (5pi)/4}` - Mathematics

Advertisements
Advertisements

प्रश्न

Evaluate the following:

`cos^-1{cos  (5pi)/4}`

Advertisements

उत्तर

We know

`cos^-1(costheta)=thetaif 0<=theta<=pi`

We have

`cos^-1{cos  (5pi)/4}=cos^-1{cos(2pi-(3pi)/4)}`

`=cos^-1{cos((3pi)/4)}`

`=(3pi)/4`

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 2.2 | पृष्ठ ४२

वीडियो ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्न

​Find the principal values of the following:

`cos^-1(tan  (3pi)/4)`


`sin^-1(sin  (5pi)/6)`


`sin^-1(sin4)`


Evaluate the following:

`cos^-1(cos3)`


Evaluate the following:

`cos^-1(cos5)`


Evaluate the following:

`tan^-1(tan2)`


Evaluate the following:

`tan^-1(tan4)`


Evaluate the following:

`sec^-1(sec  (5pi)/4)`


Evaluate the following:

`cosec^-1(cosec  (13pi)/6)`


Evaluate the following:

`cot^-1(cot  (4pi)/3)`


Evaluate the following:

`cot^-1{cot  ((21pi)/4)}`


Write the following in the simplest form:

`tan^-1{(sqrt(1+x^2)-1)/x},x !=0`


Write the following in the simplest form:

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


Write the following in the simplest form:

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


Evaluate the following:

`sin(sin^-1  7/25)`

 


Prove the following result-

`tan^-1  63/16 = sin^-1  5/13 + cos^-1  3/5`


Evaluate:

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


Evaluate:

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


Evaluate:

`cos(sec^-1x+\text(cosec)^-1x)`,|x|≥1


`tan^-1x+2cot^-1x=(2x)/3`


Solve the following equation for x:

 cot−1x − cot−1(x + 2) =`pi/12`, > 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`


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


Evaluate the following:

`sin(1/2cos^-1  4/5)`


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


`2tan^-1  1/5+tan^-1  1/8=tan^-1  4/7`


Prove that

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


If `sin^-1  (2a)/(1+a^2)+sin^-1  (2b)/(1+b^2)=2tan^-1x,` Prove that  `x=(a+b)/(1-ab).`


Solve the following equation for x:

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


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


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


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


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


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


If α = \[\tan^{- 1} \left( \tan\frac{5\pi}{4} \right) \text{ and }\beta = \tan^{- 1} \left( - \tan\frac{2\pi}{3} \right)\] , then

 

\[\tan^{- 1} \frac{1}{11} + \tan^{- 1} \frac{2}{11}\]  is equal to

 

 


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


Find the value of `sin^-1(cos((33π)/5))`.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×