Advertisements
Advertisements
प्रश्न
Find the principal value of the following: cosec- 1(2)
उत्तर
The principal value branch of cosec-1x is `[- pi/2, pi/2] - {0}`.
Let cosec-1(2) = α, `"where" (-pi)/(2) ≤ α ≤ pi/(2)`, α ≠ 0.
∴ cosec α = 2 = `"cosec" pi/(6)`
∴ α = `pi/(6) ...[ ∵ - pi/2 ≤ pi/6 ≤ pi/2 ]`
∴ the principal value of cosec-1(2) is `pi/(6)`.
APPEARS IN
संबंधित प्रश्न
If `sin^-1(1-x) -2sin^-1x = pi/2` then x is
- -1/2
- 1
- 0
- 1/2
Find the principal value of cosec−1 (2)
Find the value of the following:
`tan^(-1)(1) + cos^(-1) (-1/2) + sin^(-1) (-1/2)`
Find the value of the following:
`cos^(-1) (cos (13pi)/6)`
Find the value of the following:
`tan^(-1) (tan (7x)/6)`
`sin^-1{cos(sin^-1 sqrt3/2)}`
Find the domain of the following function:
`f(x)sin^-1sqrt(x^2-1)`
If `sin^-1 x + sin^-1 y+sin^-1 z+sin^-1 t=2pi` , then find the value of x2 + y2 + z2 + t2
Evaluate the following:
`tan^-1(-1/sqrt3)+tan^-1(-sqrt3)+tan^-1(sin(-pi/2))`
Evaluate the following:
`cot^-1{2cos(sin^-1 sqrt3/2)}`
In ΔABC, if a = 18, b = 24, c = 30 then find the values of sin `(A/2)`.
In ΔABC, if a = 18, b = 24, c = 30 then find the values of tan `A/2`
In ΔABC prove that `sin "A"/(2). sin "B"/(2). sin "C"/(2) = ["A(ΔABC)"]^2/"abcs"`
Find the principal value of the following: tan- 1( - √3)
Find the principal value of the following: cos- 1`(-1/2)`
Evaluate the following:
`tan^-1(1) + cos^-1(1/2) + sin^-1(1/2)`
Evaluate the following:
`tan^-1 sqrt(3) - sec^-1 (-2)`
Evaluate the following:
`"cosec"^-1(-sqrt(2)) + cot^-1(sqrt(3))`
Prove the following:
`sin^-1(1/sqrt(2)) -3sin^-1(sqrt(3)/2) = -(3π)/(4)`
Prove the following:
`sin^-1(3/5) + cos^-1(12/13) = sin^-1(56/65)`
In ΔABC, prove the following:
`(cos A)/a + (cos B)/b + (cos C)/c = (a^2 + b^2 + c^2)/(2abc)`
If `sin(sin^-1(1/5) + cos^-1(x))` = 1, then x = ______
Evaluate cot(tan−1(2x) + cot−1(2x))
Find the principal value of the following:
cosec-1 (2)
Show that `tan^-1 (1/2) + tan^-1 (2/11) = tan^-1 (3/4)`
Evaluate:
`cos[tan^-1 (3/4)]`
If `sin^-1(x/13) + cosec^-1(13/12) = pi/2`, then the value of x is ______
sin[3 sin-1 (0.4)] = ______.
Which of the following function has period 2?
If `sin^-1x + cos^-1y = (3pi)/10,` then `cos^-1x + sin^-1y =` ______
In a triangle ABC, ∠C = 90°, then the value of `tan^-1 ("a"/("b + c")) + tan^-1("b"/("c + a"))` is ______.
If `3tan^-1x +cot^-1x = pi`, then xis equal to ______.
Solve for x `tan^-1((1 - x)/(1 + x)) = 1/2 tan^-1x, x > 0`
The domain of y = cos–1(x2 – 4) is ______.
Show that `2tan^-1 (-3) = (-pi)/2 + tan^-1 ((-4)/3)`
Show that `cos(2tan^-1 1/7) = sin(4tan^-1 1/3)`
Show that `sin^-1 5/13 + cos^-1 3/5 = tan^-1 63/16`
`"sin"^2 25° + "sin"^2 65°` is equal to ____________.
`("cos" 8° - "sin" 8°)/("cos" 8° + "sin" 8°)` is equal to ____________.
If `"cos"^-1 "x + sin"^-1 "x" = pi`, then the value of x is ____________.
If tan-1 3 + tan-1 x = tan-1 8, then x = ____________.
`"sin"^-1 (-1/2)`
`"cos"^-1 1/2 + 2 "sin"^-1 1/2` is equal to ____________.
`"sin"^-1 (1 - "x") - 2 "sin"^-1 "x" = pi/2`
`sin[π/3 - sin^-1 (-1/2)]` is equal to:
`2"tan"^-1 ("cos x") = "tan"^-1 (2 "cosec x")`
If a = `(2sin theta)/(1 + costheta + sintheta)`, then `(1 + sintheta - costheta)/(1 + sintheta)` is
Which of the following functions is inverse of itself?
The number of solutions of sin–1x + sin–1(1 – x) = cos–1x is
The inverse of `f(x) = sqrt(3x^2 - 4x + 5)` is
What is the value of `sin^-1(sin (3pi)/4)`?
What is the principal value of cosec–1(2).
`tan^-1 (1 - x)/(1 + x) = 1/2tan^-1x, (x > 0)`, x then will be equal to.
`2tan^-1 (cos x) = tan^-1 (2"cosec" x)`, then 'x' will be equal to
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)
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)
cos–1(cos10) is equal to ______.
If ax + b (sec (tan–1 x)) = c and ay + b (sec.(tan–1 y)) = c, then `(x + y)/(1 - xy)` = ______.
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 ______.
If 2 tan–1 (cosx) = tan–1 (2 cosec x), then sin x + cos x is equal to ______.
sin [cot–1 (cos (tan–1 x))] = ______.
If y = `tan^-1 (sqrt(1 + x^2) - sqrt(1 - x^2))/(sqrt(1 + x^2) + sqrt(1 - x^2))`, then `dy/dx` is equal to ______.
`sin[π/3 + sin^-1 (1/2)]` is equal to ______.
Solve for x:
5tan–1x + 3cot–1x = 2π
Find the value of `tan^-1(x/y) + tan^-1((y - x)/(y + x))`
