Advertisements
Advertisements
Question
The domain of the function defined by f(x) = sin–1x + cosx is ______.
Options
[–1, 1]
[–1, π + 1]
`(– oo, oo)`
φ
Solution
The domain of the function defined by f(x) = sin–1x + cosx is [–1, 1].
Explanation:
The domain of cos is R and the domain of sin–1 is [–1, 1].
Therefore, the domain of cosx + sin–1x is R ∩ [–1,1]
i.e., [–1, 1].
APPEARS IN
RELATED QUESTIONS
Show that `2sin^-1(3/5) = tan^-1(24/7)`
Find the value of the following:
If sin−1 x = y, then
Evaluate the following:
`cot^-1{2cos(sin^-1 sqrt3/2)}`
In ΔABC, if a = 18, b = 24, c = 30 then find the values of cos `A/2`
Find the principal value of the following: `sin^-1 (1/2)`
Prove the following:
`sin^-1(-1/2) + cos^-1(-sqrt(3)/2) = cos^-1(-1/2)`
In ΔABC, prove the following:
`(cos A)/a + (cos B)/b + (cos C)/c = (a^2 + b^2 + c^2)/(2abc)`
Find the principal value of the following:
tan-1 (-1)
Find the principal value of `sec^-1 (- sqrt(2))`
The value of cot `(tan^-1 2x + cot^-1 2x)` is ______
The principle solutions of equation tan θ = -1 are ______
sin[3 sin-1 (0.4)] = ______.
If sin `(sin^-1 1/3 + cos^-1 x) = 1`, then the value of x 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))` = ______.
`sin{tan^-1((1 - x^2)/(2x)) + cos^-1((1 - x^2)/(1 + x^2))}` is equal to ______
Solve the following equation `cos(tan^-1x) = sin(cot^-1 3/4)`
`"sin"^2 25° + "sin"^2 65°` is equal to ____________.
`2"tan"^-1 ("cos x") = "tan"^-1 (2 "cosec x")`
If A = `[(cosx, sinx),(-sinx, cosx)]`, then A1 A–1 is
Which of the following functions is inverse of itself?
The number of solutions of sin–1x + sin–1(1 – x) = cos–1x is
`sin(tan^-1x), |x| < 1` is equal to
`tan^-1 (1 - x)/(1 + x) = 1/2tan^-1x, (x > 0)`, x then will be equal to.
`lim_(n→∞)tan{sum_(r = 1)^n tan^-1(1/(1 + r + r^2))}` is equal to ______.
The value of cos (2cos–1 x + sin–1 x) at x = `1/5` is ______.
The value of `cos^-1(cos(π/2)) + cos^-1(sin((2π)/2))` is ______.
The value of `tan(cos^-1 4/5 + tan^-1 2/3)` is ______.
Find the value of `sin(2cos^-1 sqrt(5)/3)`.
