Advertisements
Advertisements
प्रश्न
Which of the following is the principal value branch of cosec–1x?
पर्याय
`((-pi)/2, pi/2)`
`[0, pi] - {pi/2}`
`[(-pi)/2, pi/2]`
`[(-pi)/2, pi/2] - {0}`
Advertisements
उत्तर
`[(-pi)/2, pi/2] - {0}`
Explanation:
Principal value branch of cosec–1x is
`[(-pi)/2, pi/2] - {0}` as cosec–1(0) = `oo` (not defined).
APPEARS IN
संबंधित प्रश्न
Prove that `sin^(-1) (3/5) + cos^(-1) (12/13) = sin^(-1) (56/65)`
Find the principal value of the following:
`sin^-1(-sqrt3/2)`
Find the principal value of the following:
`sin^-1(tan (5pi)/4)`
For the principal value, evaluate of the following:
`sin^-1(-1/2)+2cos^-1(-sqrt3/2)`
For the principal value, evaluate of the following:
`tan^-1(-1)+cos^-1(-1/sqrt2)`
Find the principal value of the following:
`sec^-1(-sqrt2)`
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(2cos (2pi)/3)`
For the principal value, evaluate the following:
`sin^-1[cos{2\text(cosec)^-1(-2)}]`
For the principal value, evaluate the following:
`cosec^-1(2tan (11pi)/6)`
Show that `"sin"^-1(5/13) + "cos"^-1(3/5) = "tan"^-1(63/16)`
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 | y | 80 | 120 | 28 |
Find the value of `cos^-1(cos (13pi)/6)`.
Find the value of `sec(tan^-1 y/2)`
Find value of tan (cos–1x) and hence evaluate `tan(cos^-1 8/17)`
Find the value of `sin[2cot^-1 ((-5)/12)]`
Which of the following corresponds to the principal value branch of tan–1?
The principal value of the expression cos–1[cos (– 680°)] is ______.
The value of cot (sin–1x) is ______.
The principal value of `sin^-1 ((-sqrt(3))/2)` is ______.
Find the value of `tan^-1 (tan (5pi)/6) +cos^-1(cos (13pi)/6)`
Find the value of the expression `sin(2tan^-1 1/3) + cos(tan^-1 2sqrt(2))`
Find the value of `4tan^-1 1/5 - tan^-1 1/239`
The domain of the function defined by f(x) = `sin^-1 sqrt(x- 1)` is ______.
If `cos(sin^-1 2/5 + cos^-1x)` = 0, then x is equal to ______.
The value of sin (2 tan–1(0.75)) is equal to ______.
The value of the expression `2 sec^-1 2 + sin^-1 (1/2)` is ______.
The result `tan^1x - tan^-1y = tan^-1 ((x - y)/(1 + xy))` is true when value of xy is ______.
The domain of trigonometric functions can be restricted to any one of their branch (not necessarily principal value) in order to obtain their inverse functions.
If `5 sin theta = 3 "then", (sec theta + tan theta)/(sec theta - tan theta)` is equal to ____________.
`2 "cos"^-1 "x = sin"^-1 (2"x" sqrt(1 - "x"^2))` is true for ____________.
Which of the following is the principal value branch of `"cos"^-1 "x"`
Assertion (A): Maximum value of (cos–1 x)2 is π2.
Reason (R): Range of the principal value branch of cos–1 x is `[(-π)/2, π/2]`.
