Advertisements
Advertisements
Question
Find the principal value of the following:
cosec−1 (2)
Advertisements
Solution
Let cosec−1 (2) = y
Then, cosec y = 2 = `"cosec" (pi/6)`
We know that the range of the principal value branch of cosec−1 is `[-pi/2, pi/2] - {0}`.
Therefore, the principal value of cosec−1 (2) is `pi/6`.
APPEARS IN
RELATED QUESTIONS
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{cos(sin^-1 sqrt3/2)}`
Evaluate the following:
`tan^-1 1+cos^-1 (-1/2)+sin^-1(-1/2)`
Prove the following:
`sin^-1(3/5) + cos^-1(12/13) = sin^-1(56/65)`
Prove the following:
`tan^-1(1/2) + tan^-1(1/3) = pi/(4)`
The principal value of cos−1`(-1/2)` is ______
If tan−1x + tan−1y + tan−1z = π, then show that `1/(xy) + 1/(yz) + 1/(zx)` = 1
Prove that sin `[tan^-1 ((1 - x^2)/(2x)) + cos^-1 ((1 - x^2)/(1 + x^2))]` = 1
Show that `sin^-1(3/5) + sin^-1(8/17) = cos^-1(36/85)`
Find the principal value of the following:
`sin^-1 (- 1/2)`
Find the principal value of the following:
`sec^-1 (-sqrt2)`
Evaluate:
`cos[tan^-1 (3/4)]`
Find the principal value of `sec^-1 (- sqrt(2))`
lf `sqrt3costheta + sintheta = sqrt2`, then the general value of θ is ______
sin[3 sin-1 (0.4)] = ______.
If `sin^-1 3/5 + cos^-1 12/13 = sin^-1 P`, then P is equal to ______
If 2tan-1 (cos x) = tan-1 (cosec2 x), then x = ______.
The value of cot (- 1110°) is equal to ______.
In a triangle ABC, ∠C = 90°, then the value of `tan^-1 ("a"/("b + c")) + tan^-1("b"/("c + a"))` is ______.
`cos(2sin^-1 3/4+cos^-1 3/4)=` ______.
`(sin^-1(-1/2) + tan^-1(-1/sqrt(3)))/(sec^-1 (-2/sqrt(3)) + cos^-1(1/sqrt(2))` = ______.
The domain of the function y = sin–1 (– x2) is ______.
Show that `sin^-1 5/13 + cos^-1 3/5 = tan^-1 63/16`
If `"sin"^-1("x"^2 - 7"x" + 12) = "n"pi, AA "n" in "I"`, then x = ____________.
`"sin"^-1 (-1/2)`
The range of sin-1 x + cos-1 x + tan-1 x is ____________.
The equation 2cos-1 x + sin-1 x `= (11pi)/6` has ____________.
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 ____________.
`sin[π/3 - sin^-1 (-1/2)]` is equal to:
`"tan"^-1 sqrt3 - "sec"^-1 (-2)` is equal to ____________.
sin 6θ + sin 4θ + sin 2θ = 0, then θ =
If `sin(sin^-1 1/5 + cos^-1 x) = 1`, the what will be the value of x?
If f'(x) = x–1, then find f(x)
`lim_(n→∞)tan{sum_(r = 1)^n tan^-1(1/(1 + r + r^2))}` is equal to ______.
If θ = `sin^-1((2x)/(1 + x^2)) + cos^-1((1 - x^2)/(1 + x^2))`, for `x ≥ 3/2` then the absolute value of `((cosθ + tanθ + 4)/secθ)` is ______.
If cos–1 x > sin–1 x, then ______.
Find the value of `cos(x/2)`, if tan x = `5/12` and x lies in third quadrant.
