Advertisements
Advertisements
Question
Find the principal value of the following:
`cosec^-1(-sqrt2)`
Solution
Let `cosec^-1(-sqrt2)=y`
Then,
`cosecy=-sqrt2`
We know that the range of the principal value branch is `[-pi/2,pi/2]-{0}`.
Thus,
`cosecy=-sqrt2=cosec(-pi/4)`
`y=-pi/4in [-pi/2,pi/2],y!=0`
Hence, the principal value of `cosec^-1(-sqrt2) is -pi/4.`
APPEARS IN
RELATED QUESTIONS
Prove that `sin^(-1) (3/5) + cos^(-1) (12/13) = sin^(-1) (56/65)`
if `tan^(-1) a + tan^(-1) b + tan^(-1) x = pi`, prove that a + b + c = abc
For the principal value, evaluate of the following:
`cos^-1 1/2+2sin^-1 (1/2)`
Find the principal value of the following:
`tan^-1(1/sqrt3)`
Find the principal value of the following:
`tan^-1(cos pi/2)`
For the principal value, evaluate the following:
`sin^-1(-sqrt3/2)-2sec^-1(2tan pi/6)`
For the principal value, evaluate the following:
`sec^-1(sqrt2)+2\text{cosec}^-1(-sqrt2)`
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(-1/sqrt3)`
Find the principal value of the following:
`cot^-1(tan (3pi)/4)`
If `sin^-1"x" + tan^-1"x" = pi/2`, prove that `2"x"^2 + 1 = sqrt5`
Find the value of `tan^-1 (tan (9pi)/8)`.
Find the value of `sec(tan^-1 y/2)`
Find the values of x which satisfy the equation sin–1x + sin–1(1 – x) = cos–1x.
The principal value branch of sec–1 is ______.
The value of `sin^-1 (cos((43pi)/5))` is ______.
One branch of cos–1 other than the principal value branch corresponds to ______.
The value of tan2 (sec–12) + cot2 (cosec–13) is ______.
Find the value of `tan^-1 (tan (5pi)/6) +cos^-1(cos (13pi)/6)`
Which of the following is the principal value branch of cosec–1x?
The domain of the function cos–1(2x – 1) is ______.
The value of `cos^-1 (cos (3pi)/2)` is equal to ______.
The value of `cot[cos^-1 (7/25)]` is ______.
The principal value of `cos^-1 (- 1/2)` is ______.
If `cos(tan^-1x + cot^-1 sqrt(3))` = 0, then value of x is ______.
The principal value of `tan^-1 sqrt(3)` is ______.
The least numerical value, either positive or negative of angle θ is called principal value of the inverse trigonometric function.
The minimum value of n for which `tan^-1 "n"/pi > pi/4`, n ∈ N, is valid is 5.
If `5 sin theta = 3 "then", (sec theta + tan theta)/(sec theta - tan theta)` is equal to ____________.
The general solution of the equation `"cot" theta - "tan" theta = "sec" theta` is ____________ where `(n in I).`
If `"tan"^-1 ("a"/"x") + "tan"^-1 ("b"/"x") = pi/2,` then x is equal to ____________.
Which of the following is the principal value branch of `"cos"^-1 "x"`
What is the value of x so that the seven-digit number 8439 × 53 is divisible by 99?
