English

The value of sin-1[cos(33π5)] is ______. - Mathematics

Advertisements
Advertisements

Question

The value of `sin^-1 [cos((33pi)/5)]` is ______.

Options

  • `(3pi)/5`

  • `(-7pi)/5`

  • `pi/10`

  • `(-pi)/10`

MCQ
Fill in the Blanks
Advertisements

Solution

The value of `sin^-1 [cos((33pi)/5)]` is `(-pi)/10`.

Explanation:

`sin^-1 [cos((33pi)/5)] = sin^-1[cos(6pi + (3pi)/5)]`

= `sin^-1[cos  (3pi)/5]` .......[∵ cos(2nπ + x) = cos x]

= `sin^-1 [cos(pi/2 + pi/10)]`

= `sin^-1[-sin (pi/10)]`  ......`[because cos(pi/2 + theta) = - sin theta]`

= `sin^-1[sin((-pi)/10)]`

= `(-pi)/10`

shaalaa.com
  Is there an error in this question or solution?
Chapter 2: Inverse Trigonometric Functions - Exercise [Page 37]

APPEARS IN

NCERT Exemplar Mathematics [English] Class 12
Chapter 2 Inverse Trigonometric Functions
Exercise | Q 23 | Page 37

RELATED QUESTIONS

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


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


Find the principal value of the following:

`sin^-1(cos  (2pi)/3)`


Find the principal value of the following:

`sin^-1(cos  (3pi)/4)`


For the principal value, evaluate of the following:

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


Find the principal value of the following:

`tan^-1(1/sqrt3)`


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(2tan  (3pi)/4)`


For the principal value, evaluate the following:

`sin^-1(-sqrt3/2)-2sec^-1(2tan  pi/6)`


​Find the principal value of the following:

`cosec^-1(-sqrt2)`


​Find the principal value of the following:

`\text(cosec)^-1(2/sqrt3)`


​Find the principal value of the following:

`cosec^-1(2cos  (2pi)/3)`


Find the principal value of the following:

`cot^-1(sqrt3)`


Find the principal value of the following:

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


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


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


Which of the following corresponds to the principal value branch of tan–1?


One branch of cos–1 other than the principal value branch corresponds to ______.


The domain of sin–1 2x is ______.


The principal value of `sin^-1 ((-sqrt(3))/2)` is ______.


The greatest and least values of (sin–1x)2 + (cos–1x)2 are respectively ______.


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


The value of `tan(cos^-1  3/5 + tan^-1  1/4)` is ______.


The value of the expression sin [cot–1 (cos (tan–11))] is ______.


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


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


The domain of the function defined by f(x) = `sin^-1 sqrt(x- 1)` is ______.


The value of `sin^-1 (sin  (3pi)/5)` is ______.


The principal value of `tan^-1 sqrt(3)` is ______.


The result `tan^1x - tan^-1y = tan^-1 ((x - y)/(1 + xy))` is true when value of xy is ______.


The period of the function f(x) = cos4x + tan3x is ____________.


If sin `("sin"^-1 1/5 + "cos"^-1 "x") = 1,` then the value of x is ____________.


`"cos" ["tan"^-1 {"sin" ("cot"^-1  "x")}]` is equal to ____________.


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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×