English

Evaluate: `Cos(Sec^-1x+Cosec^-1x)` - Mathematics

Advertisements
Advertisements

Question

Evaluate:

`cos(sec^-1x+\text(cosec)^-1x)`,|x|≥1

Sum

Solution

`cos(sec^-1x+\text(cosec)^-1x)`

`=cos(pi/2)`         `[thereforesec^-1x+\text(cosec)^-1x=pi/2]`

= 0

 

shaalaa.com
  Is there an error in this question or solution?
Chapter 4: Inverse Trigonometric Functions - Exercise 4.10 [Page 66]

APPEARS IN

RD Sharma Mathematics [English] Class 12
Chapter 4 Inverse Trigonometric Functions
Exercise 4.10 | Q 1.5 | Page 66

RELATED QUESTIONS

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`


If `cos^-1( x/a) +cos^-1 (y/b)=alpha` , prove that `x^2/a^2-2(xy)/(ab) cos alpha +y^2/b^2=sin^2alpha`


Solve for x:

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


`sin^-1(sin  (13pi)/7)`


Evaluate the following:

`cos^-1{cos  (13pi)/6}`


Evaluate the following:

`tan^-1(tan  (6pi)/7)`


Evaluate the following:

`tan^-1(tan  (9pi)/4)`


Evaluate the following:

`tan^-1(tan2)`


Evaluate the following:

`tan^-1(tan12)`


Evaluate the following:

`cot^-1(cot  (19pi)/6)`


Write the following in the simplest form:

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

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


Evaluate the following:

`sin(sin^-1  7/25)`

 


Evaluate the following:

`sec(sin^-1  12/13)`


`5tan^-1x+3cot^-1x=2x`


Solve the following:

`sin^-1x+sin^-1  2x=pi/3`


Solve `cos^-1sqrt3x+cos^-1x=pi/2`


`sin^-1  4/5+2tan^-1  1/3=pi/2`


`4tan^-1  1/5-tan^-1  1/239=pi/4`


Prove that

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


Find the value of the following:

`tan^-1{2cos(2sin^-1  1/2)}`


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


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


Write the range of tan−1 x.


Write the value of cos−1 \[\left( \tan\frac{3\pi}{4} \right)\]


Write the principal value of `tan^-1sqrt3+cot^-1sqrt3`


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


Write the value of \[\cos\left( \sin^{- 1} x + \cos^{- 1} x \right), \left| x \right| \leq 1\]


The value of tan \[\left\{ \cos^{- 1} \frac{1}{5\sqrt{2}} - \sin^{- 1} \frac{4}{\sqrt{17}} \right\}\] is

 


The positive integral solution of the equation
\[\tan^{- 1} x + \cos^{- 1} \frac{y}{\sqrt{1 + y^2}} = \sin^{- 1} \frac{3}{\sqrt{10}}\text{ is }\]


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

 


Find the real solutions of the equation
`tan^-1 sqrt(x(x + 1)) + sin^-1 sqrt(x^2 + x + 1) = pi/2`


The value of sin `["cos"^-1 (7/25)]` is ____________.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×