मराठी

Evaluate the Following: `Cos^-1(Cos4)` - Mathematics

Advertisements
Advertisements

प्रश्न

Evaluate the following:

`cos^-1(cos4)`

उत्तर

We know

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

We have

`cos^-1(cos4)=cos^-1{cos(2pi-4)}`

= 2π - 4

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 4: Inverse Trigonometric Functions - Exercise 4.07 [पृष्ठ ४२]

APPEARS IN

आरडी शर्मा Mathematics [English] Class 12
पाठ 4 Inverse Trigonometric Functions
Exercise 4.07 | Q 2.6 | पृष्ठ ४२

व्हिडिओ ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्‍न

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 principal values of the following:

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


`sin^-1(sin  pi/6)`


Evaluate the following:

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


Evaluate the following:

`cos^-1(cos12)`


Evaluate the following:

`tan^-1(tan  pi/3)`


Evaluate the following:

`sec^-1(sec  pi/3)`


Evaluate the following:

`sec^-1(sec  (9pi)/5)`


Evaluate the following:

`cosec^-1(cosec  (13pi)/6)`


Evaluate the following:

`cot^-1(cot  pi/3)`


Write the following in the simplest form:

`cot^-1  a/sqrt(x^2-a^2),|  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(tan^-1  24/7)`


Solve: `cos(sin^-1x)=1/6`


Evaluate:

`cos(tan^-1  3/4)`


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


`4sin^-1x=pi-cos^-1x`


Solve the following equation for x:

tan−1(x + 1) + tan−1(x − 1) = tan−1`8/31`


Solve the following equation for x:

tan−1`((1-x)/(1+x))-1/2` tan−1x = 0, where x > 0


Sum the following series:

`tan^-1  1/3+tan^-1  2/9+tan^-1  4/33+...+tan^-1  (2^(n-1))/(1+2^(2n-1))`


Solve the following equation for x:

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


If `sin^-1x+sin^-1y+sin^-1z=(3pi)/2,`  then write the value of x + y + z.


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


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


Write the value of

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


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


If \[\tan^{- 1} (\sqrt{3}) + \cot^{- 1} x = \frac{\pi}{2},\] find x.


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

 


What is the principal value of `sin^-1(-sqrt3/2)?`


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


Write the principal value of \[\cos^{- 1} \left( \cos680^\circ  \right)\]


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


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) = 


The value of sin \[\left( \frac{1}{4} \sin^{- 1} \frac{\sqrt{63}}{8} \right)\] is

 


If \[\sin^{- 1} \left( \frac{2a}{1 - a^2} \right) + \cos^{- 1} \left( \frac{1 - a^2}{1 + a^2} \right) = \tan^{- 1} \left( \frac{2x}{1 - x^2} \right),\text{ where }a, x \in \left( 0, 1 \right)\] , then, the value of x is

 


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.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×