Advertisements
Advertisements
प्रश्न
Find the domain of the following function:
`f(x)=sin^-1x^2`
उत्तर
To the domain of sin-1 which is [−1, 1]
∴ x2 ∈ [0, 1] as x2 can not be negative
∴ x ∈ [-1, 1]
Hence, the domain is [−1, 1]
APPEARS IN
संबंधित प्रश्न
Find the principal value of `tan^(-1) (-sqrt3)`
Find the value of the following:
If sin−1 x = y, then
Find the principal value of `sin^-1(1/sqrt2)`
Evaluate the following:
`tan^-1(-1/sqrt3)+tan^-1(-sqrt3)+tan^-1(sin(-pi/2))`
Evaluate: tan `[ 2 tan^-1 (1)/(2) – cot^-1 3]`
In ΔABC, if a = 18, b = 24, c = 30 then find the values of cos `A/2`
Evaluate the following:
`tan^-1(1) + cos^-1(1/2) + sin^-1(1/2)`
Prove the following:
`cos^-1(3/5) + cos^-1(4/5) = pi/(2)`
In ΔABC, prove the following:
`(cos A)/a + (cos B)/b + (cos C)/c = (a^2 + b^2 + c^2)/(2abc)`
Find the principal solutions of the following equation:
sin 2θ = `− 1/(sqrt2)`
Find the principal value of the following:
cosec-1 (2)
Show that `tan^-1 (1/2) + tan^-1 (2/11) = tan^-1 (3/4)`
Express `tan^-1 [(cos x)/(1 - sin x)], - pi/2 < x < (3pi)/2` in the simplest form.
The value of cot `(tan^-1 2x + cot^-1 2x)` is ______
In ΔABC, tan`A/2 = 5/6` and tan`C/2 = 2/5`, then ______
In Δ ABC, with the usual notations, if sin B sin C = `"bc"/"a"^2`, then the triangle is ______.
Which of the following function has period 2?
If `sin^-1 3/5 + cos^-1 12/13 = sin^-1 P`, then P is equal to ______
The principal value of `tan^{-1(sqrt3)}` is ______
The principal value of `sin^-1 (sin (3pi)/4)` is ______.
If `3sin^-1((2x)/(1 + x^2)) - 4cos^-1((1 - x^2)/(1 + x^2)) + 2tan^-1((2x)/(1 - x^2)) = pi/3`, then x is equal to ______
`cos^-1 4/5 + tan^-1 3/5` = ______.
Solve for x `tan^-1((1 - x)/(1 + x)) = 1/2 tan^-1x, x > 0`
If 2 tan–1(cos θ) = tan–1(2 cosec θ), then show that θ = π 4, where n is any integer.
All trigonometric functions have inverse over their respective domains.
`"cos" 2 theta` is not equal to ____________.
If tan-1 (x – 1) + tan-1 x + tan-1 (x + 1) = tan-1 3x, then the values of x are ____________.
`"sin"^-1 (1 - "x") - 2 "sin"^-1 "x" = pi/2`
`"sin" ["cot"^-1 {"cos" ("tan"^-1 "x")}] =` ____________.
`2"tan"^-1 ("cos x") = "tan"^-1 (2 "cosec x")`
`"tan"^-1 sqrt3 - "sec"^-1 (-2)` is equal to ____________.
Which of the following functions is inverse of itself?
If `(-1)/sqrt(2) ≤ x ≤ 1/sqrt(2)` then `sin^-1 (2xsqrt(1 - x^2))` is equal to
`2tan^-1 (cos x) = tan^-1 (2"cosec" x)`, then 'x' will be equal to
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 ______.
`cot^-1(sqrt(cos α)) - tan^-1 (sqrt(cos α))` = x, then sin x = ______.
`sin[π/3 + sin^-1 (1/2)]` is equal to ______.
If tan 4θ = `tan(2/θ)`, then the general value of θ is ______.
