Advertisements
Advertisements
प्रश्न
Find the principal value of the following:
`\text(cosec)^-1(2/sqrt3)`
Advertisements
उत्तर
Let `\text(cosec)^-1(2/sqrt3)=y`
Then,
`\text(cosec) y=2/sqrt3`
We know that the range of the principal value branch is `[-pi/2,pi/2]-{0}`
Thus,
`\text(cosec) y=2/sqrt3=text(cosec)(pi/3)`
`=>y=pi/3in[-pi/2,pi/2],y!=0`
Hence, the principal value of `\text(cosec)^-1(2/sqrt3) is pi/3`
APPEARS IN
संबंधित प्रश्न
Write the principal value of `tan^(-1)+cos^(-1)(-1/2)`
Find the value of `tan^(-1) sqrt3 - cot^(-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)`
For the principal value, evaluate of the following:
`tan^-1{2sin(4cos^-1 sqrt3/2)}`
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(-sqrt3/2)+\text{cosec}^-1(-2/sqrt3)`
Find the principal value of the following:
`cot^-1(-sqrt3)`
Find the principal value of the following:
`cot^-1(sqrt3)`
if sec-1 x = cosec-1 v. show that `1/x^2 + 1/y^2 = 1`
Find the principal value of cos–1x, for x = `sqrt(3)/2`.
Find the value of `tan^-1 (tan (9pi)/8)`.
Prove that tan(cot–1x) = cot(tan–1x). State with reason whether the equality is valid for all values of x.
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)]`
The value of `sin^-1 (cos((43pi)/5))` is ______.
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 ______.
Let θ = sin–1 (sin (– 600°), then value of θ is ______.
Find the value of `tan^-1 (tan (5pi)/6) +cos^-1(cos (13pi)/6)`
Find the value of `tan^-1 (- 1/sqrt(3)) + cot^-1(1/sqrt(3)) + tan^-1(sin((-pi)/2))`
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 value of `cos^-1 (cos (3pi)/2)` is equal to ______.
The set of values of `sec^-1 (1/2)` is ______.
The result `tan^1x - tan^-1y = tan^-1 ((x - y)/(1 + xy))` is true when value of xy is ______.
The value of the expression (cos–1x)2 is equal to sec2x.
The principal value of `sin^-1 [cos(sin^-1 1/2)]` is `pi/3`.
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 sin `("sin"^-1 1/5 + "cos"^-1 "x") = 1,` then the value of x is ____________.
If `"tan"^-1 ("a"/"x") + "tan"^-1 ("b"/"x") = pi/2,` then x is equal to ____________.
`"sec" {"tan"^-1 (-"y"/3)}` is equal to ____________.
What is the value of `tan^-1(1) cos^-1(- 1/2) + sin^-1(- 1/2)`
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]`.
