Advertisements
Advertisements
प्रश्न
Find the principal value of the following:
`"cosec"^(-1)(-sqrt2)`
Advertisements
उत्तर
Let `"cosec"^(-1)(-sqrt2)` = y
Then, cosec y = `-sqrt2 = - "cosec" (pi/4) = "cosec" (-pi/4)`
We know that the range of the principal value branch of cosec−1 is `[-pi/2,pi/2] - {0}` and `"cosec"(-pi/4) = -sqrt2`.
Therefore, the principal value of `"cosec"^(-1) (-sqrt2)` is `-pi/4`.
APPEARS IN
संबंधित प्रश्न
If `tan^-1((x-1)/(x-2))+cot^-1((x+2)/(x+1))=pi/4; `
Find the principal value of the following:
`cot^(-1) (sqrt3)`
Prove that:
`tan^-1 ((sqrt(1 + x) - sqrt(1 - x))/(sqrt(1 + x) + sqrt(1 - x))) = pi/4 - 1/2 cos^-1 x`, for `- 1/sqrt2 ≤ x ≤ 1`
[Hint: Put x = cos 2θ]
`sin^-1 1/2-2sin^-1 1/sqrt2`
Find the domain of the following function:
`f(x)=sin^-1x^2`
Find the domain of the following function:
`f(x)=sin^-1x+sin^-1 2x`
Evaluate the following:
`tan^-1(tan (5pi)/6)+cos^-1{cos((13pi)/6)}`
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`
In ΔABC, if a = 18, b = 24, c = 30 then find the values of cosA
In ΔABC, if a = 18, b = 24, c = 30 then find the values of A(ΔABC)
Find the principal value of the following: cosec- 1(2)
Prove the following:
`tan^-1["cosθ + sinθ"/"cosθ - sinθ"] = pi/(4) + θ, if θ ∈ (- pi/4, pi/4)`
Evaluate:
`sin[cos^-1 (3/5)]`
Show that `tan^-1 (1/2) + tan^-1 (2/11) = tan^-1 (3/4)`
Find the principal value of `cos^-1 sqrt(3)/2`
The value of 2 `cot^-1 1/2 - cot^-1 4/3` is ______
The value of `sin^-1(cos (53pi)/5)` is ______
Show that `sin^-1 5/13 + cos^-1 3/5 = tan^-1 63/16`
When `"x" = "x"/2`, then tan x is ____________.
If tan-1 (x – 1) + tan-1 x + tan-1 (x + 1) = tan-1 3x, then the values of x are ____________.
If `"x" in (- pi/2, pi/2), "then the value of tan"^-1 ("tan x"/4) + "tan"^-1 ((3 "sin" 2 "x")/(5 + 3 "cos" 2 "x"))` is ____________.
The number of solutions of sin–1x + sin–1(1 – x) = cos–1x is
sin 6θ + sin 4θ + sin 2θ = 0, then θ =
If `sqrt(2)` sec θ + tan θ = 1, then the general value of θ is
What is the principal value of cosec–1(2).
Values of tan–1 – sec–1(–2) is equal to
what is the value of `cos^-1 (cos (13pi)/6)`
Value of `sin(pi/3 - sin^1 (- 1/2))` is equal to
If f(x) = x5 + 2x – 3, then (f–1)1 (–3) = ______.
Consider f(x) = sin–1[2x] + cos–1([x] – 1) (where [.] denotes greatest integer function.) If domain of f(x) is [a, b) and the range of f(x) is {c, d} then `a + b + (2d)/c` is equal to ______. (where c < d)
Let x = sin–1(sin8) + cos–1(cos11) + tan–1(tan7), and x = k(π – 2.4) for an integer k, then the value of k is ______.
If sin–1a + sin–1b + sin–1c = π, then find the value of `asqrt(1 - a^2) + bsqrt(1 - b^2) + csqrt(1 - c^2)`.
If x ∈ R – {0}, then `tan^-1 ((sqrt(1 + x^2) + sqrt(1 - x^2))/(sqrt(1 + x^2) - sqrt(1 - x^2)))`
The value of `cos^-1(cos(π/2)) + cos^-1(sin((2π)/2))` is ______.
Derivative of `tan^-1(x/sqrt(1 - x^2))` with respect sin–1(3x – 4x3) is ______.
The value of `tan(cos^-1 4/5 + tan^-1 2/3)` is ______.
Find the value of `tan^-1(x/y) + tan^-1((y - x)/(y + x))`
