हिंदी

Find the principal value of sec^-1 (- sqrt(2)). - Mathematics

Advertisements
Advertisements

प्रश्न

Find the principal value of `sec^-1 (- sqrt(2))`.

योग
Advertisements

उत्तर

Let y = `sec^-1 (- sqrt(2))`

Where 0 ≤ y ≤ π

sec y = `- sqrt(2)`

`y +- pi/2`

`1/sec y = - 1/sqrt(2)` 

cos y = `- 1/sqrt(2)`

∴ The principal value of `sec^-1 (- sqrt(2)) = (3pi)/4`

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 3: Trigonometry - Exercise 3.11 [पृष्ठ १४९]

APPEARS IN

सामाचीर कलवी Mathematics - Volume 1 and 2 [English] Class 11 TN Board
अध्याय 3 Trigonometry
Exercise 3.11 | Q 1. (iv) | पृष्ठ १४९

वीडियो ट्यूटोरियलVIEW ALL [2]

संबंधित प्रश्न

Find the principal value of the following:

`cos^(-1) (-1/2)`


Find the principal value of the following:

`"cosec"^(-1)(-sqrt2)`


Find the value of the following:

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


Find the value of the following:

`tan^(-1) (tan  (7pi)/6)`


`sin^-1{cos(sin^-1  sqrt3/2)}`


Evaluate the following:

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


Evaluate the following:

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


Solve for x:
`tan^-1 [(x-1),(x-2)] + tan^-1 [(x+1),(x+2)] = x/4`


Find the principal value of the following: `sin^-1 (1/2)`


Find the principal value of the following: cosec- 1(2)


Find the principal value of the following: tan-1(– 1)


Prove the following:

`tan^-1(1/2) + tan^-1(1/3) = pi/(4)`


In ΔABC, prove the following:

`(cos A)/a + (cos B)/b + (cos C)/c = (a^2 + b^2 + c^2)/(2abc)`


The principal value of cos−1`(-1/2)` is ______


`tan^-1(tan  (7pi)/6)` = ______


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


Evaluate: `cos (sin^-1 (4/5) + sin^-1 (12/13))`


Show that `sin^-1 (- 3/5) - sin^-1 (- 8/17) = cos^-1 (84/85)`


Express `tan^-1 [(cos x)/(1 - sin x)], - pi/2 < x < (3pi)/2` in the simplest form.


Find the principal value of `sin^-1  1/sqrt(2)`


Find the principal value of `cos^-1  sqrt(3)/2`


`sin^-1x + sin^-1  1/x + cos^-1x + cos^-1  1/x` = ______


lf `sqrt3costheta + sintheta = sqrt2`, then the general value of θ is ______ 


`sin^2(sin^-1  1/2) + tan^2 (sec^-1  2) + cot^2(cosec^-1  4)` = ______.


The principal value of `sin^-1 (sin  (3pi)/4)` is ______.


The value of `cos(pi/4 + x) - cos(pi/4 - x)` is ______.


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


Prove that `tan^-1  1/4 + tan^-1  2/9 = sin^-1  1/sqrt(5)`


When `"x" = "x"/2`, then tan x is ____________.


`"sin"^2 25° +  "sin"^2 65°` is equal to ____________.


If `"x + y" = "x"/4` then (1+ tanx)(1 + tany) is equal to ____________.


`"cos"^-1 1/2 + 2  "sin"^-1  1/2` is equal to ____________.


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


3 tan-1 a is equal to ____________.


If tan-1 x – tan-1 y = tan-1 A, then A is equal to ____________.


If `"cot"^-1 (sqrt"cos" alpha) - "tan"^-1 (sqrt "cos" alpha) = "x",` then sinx is equal to ____________.


If a = `(2sin theta)/(1 + costheta + sintheta)`, then `(1 + sintheta - costheta)/(1 + sintheta)` is 


Which of the following functions is inverse of itself?


What will be the principal value of `sin^-1(-1/2)`?


what is the value of `cos^-1 (cos  (13pi)/6)`


If f'(x) = x–1, then find f(x)


If θ = `sin^-1((2x)/(1 + x^2)) + cos^-1((1 - x^2)/(1 + x^2))`, for `x ≥ 3/2` then the absolute value of `((cosθ + tanθ + 4)/secθ)` is ______.


Number of values of x satisfying the system of equations `sin^-1sqrt(2 + e^(-2x) - 2e^-x) + sec^-1sqrt(1 - x^2 + x^4) = π/2` and `5^(1+tan^-1x)` = 4 + [cos–1x] is ______ (where [.] denotes greatest integer function)


The value of cos (2cos–1 x + sin–1 x) at x = `1/5` is ______.


If 2 tan–1 (cosx) = tan–1 (2 cosec x), then sin x + cos x is equal to ______.


Find the value of `sin(2cos^-1  sqrt(5)/3)`.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×