Write the principal value of tan^(-1)+cos^(-1)(-1/2) - Mathematics and Statistics

Advertisements
Advertisements

Write the principal value of `tan^(-1)+cos^(-1)(-1/2)`

Advertisements

Solution

`Let tan^(-1)=y and cos^(-1)(-1/2)=z`

`tany=1=tan(pi/4) and cosz=-1/2=-cos(pi/3)=cos(pi-pi/3)=cos((2pi)/3)`

The ranges of principal value branch of tan−1 and cos−1 are `(-pi/2,pi/2)and[0,pi] ` respectively

`therefore tan^(-1)=pi/4 and cos^(-1)(-1/2)=2pi/3`

`therefore tan^(-1)(1)+cos^(-1)(-1/2)=pi/4+(2pi)/3=(11pi)/12`

 

  Is there an error in this question or solution?
2012-2013 (March) Delhi Set 1

RELATED QUESTIONS

The principal solution of `cos^-1(-1/2)` is :


The principal solution of the equation cot x=`-sqrt 3 ` is


Prove that `sin^(-1) (3/5) + cos^(-1) (12/13) = sin^(-1) (56/65)`


Solve `3tan^(-1)x + cot^(-1) x = pi`


if `tan^(-1) a + tan^(-1) b + tan^(-1) x = pi`, prove that a + b + c = abc 


Find the principal value of the following:

`sin^-1(-sqrt3/2)`


Find the principal value of the following:

`sin^-1(cos  (2pi)/3)`


Find the principal value of the following:

`sin^-1((sqrt3-1)/(2sqrt2))`


For the principal value, evaluate of the following:

`sin^-1(-1/2)+2cos^-1(-sqrt3/2)`


Find the principal value of the following:

`tan^-1(1/sqrt3)`


Find the principal value of the following:

`tan^-1(-1/sqrt3)`


Find the principal value of the following:

`tan^-1(cos  pi/2)`


Find the principal value of the following:

`tan^-1(2cos  (2pi)/3)`


For the principal value, evaluate of the following:

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


For the principal value, evaluate of the following:

`tan^-1{2sin(4cos^-1  sqrt3/2)}`


Find the principal value of the following:

`sec^-1(2)`


Find the principal value of the following:

`sec^-1(2tan  (3pi)/4)`


​Find the principal value of the following:

`cosec^-1(-sqrt2)`


​Find the principal value of the following:

cosec-1(-2)


For the principal value, evaluate the following:

`sin^-1[cos{2\text(cosec)^-1(-2)}]`


Find the principal value of the following:

`cot^-1(-sqrt3)`


Find the principal value of the following:

`cot^-1(sqrt3)`


Show that `"sin"^-1(5/13) + "cos"^-1(3/5) = "tan"^-1(63/16)`


Show that `"sin"^-1(5/13) + "cos"^-1(3/5) = "tan"^-1(63/16)`


if sec-1  x = cosec-1  v. show that `1/x^2 + 1/y^2 = 1`


Solve for x, if:

tan (cos-1x) = `2/sqrt5`


If `sin^-1"x" + tan^-1"x" = pi/2`, prove that `2"x"^2 + 1 = sqrt5`  


The index number by the method of aggregates for the year 2010, taking 2000 as the base year, was found to be 116. If sum of the prices in the year 2000 is ₹ 300, find the values of x and y in the data given below

Commodity A B C D E F
Price in the year 2000 (₹) 50 x 30 70 116 20
Price in the year 2010 (₹) 60 24 80  120 28

Find the value of `sin(2tan^-1  2/3) + cos(tan^-1 sqrt(3))`


The principal value branch of sec–1 is ______.


The value of sin (2 sin–1 (.6)) is ______.


The value of tan2 (sec–12) + cot2 (cosec–13) is ______.


Find the value of `tan^-1 (- 1/sqrt(3)) + cot^-1(1/sqrt(3)) + tan^-1(sin((-pi)/2))`


Which of the following is the principal value branch of cos–1x?


The domain of the function cos–1(2x – 1) is ______.


If `cos(sin^-1  2/5 + cos^-1x)` = 0, then x is equal to ______.


The value of the expression `2 sec^-1 2 + sin^-1 (1/2)` is ______.


If tan–1x + tan–1y = `(4pi)/5`, then cot–1x + cot–1y equals ______.


The set of values of `sec^-1 (1/2)` is ______.


The value of `cos^-1 (cos  (14pi)/3)` is ______.


The least numerical value, either positive or negative of angle θ is called principal value of the inverse trigonometric function.


The principal value of `sin^-1 [cos(sin^-1  1/2)]` is `pi/3`.


`2  "cos"^-1 "x = sin"^-1 (2"x" sqrt(1 - "x"^2))` is true for ____________.


`"sec" {"tan"^-1 (-"y"/3)}` is equal to ____________.


What is the value of x so that the seven-digit number 8439 × 53 is divisible by 99?


What is the principle value of `sin^-1 (1/sqrt(2))`?


What is the principal value of `cot^-1 ((-1)/sqrt(3))`?


What is the value of `tan^-1(1) cos^-1(- 1/2) + sin^-1(- 1/2)`


Evaluate `sin^-1 (sin  (3π)/4) + cos^-1 (cos π) + tan^-1 (1)`.


Share
Notifications



      Forgot password?
Use app×