Advertisements
Advertisements
Question
Find the domain of the following function:
`f(x)=sin^-1x+sin^-1 2x`
Advertisements
Solution
Let f(x) = g(x) + h(x), where g(x)=cotx and h(x)=cot−1x
Therefore, the domain of f(x) is given by the intersection of the domain of g(x) and h(x)
The domain of g(x) is [−1, 1]
The domain of h(x) is `[-1/2, 1/2]`
Therfore, the intersection of g(x) and h(x) is `[-1/2, 1/2]`
Hence, the domain is `[-1/2, 1/2]`
APPEARS IN
RELATED QUESTIONS
If `sin^-1(1-x) -2sin^-1x = pi/2` then x is
- -1/2
- 1
- 0
- 1/2
Find the principal value of the following:
cosec−1 (2)
Evaluate the following:
`tan^-1 1+cos^-1 (-1/2)+sin^-1(-1/2)`
Evaluate the following:
`cot^-1{2cos(sin^-1 sqrt3/2)}`
Evaluate the following:
`tan^-1(-1/sqrt3)+cot^-1(1/sqrt3)+tan^-1(sin(-pi/2))`
In ΔABC, if a = 18, b = 24, c = 30 then find the values of cos `A/2`
In ΔABC, if a = 18, b = 24, c = 30 then find the values of A(ΔABC)
Find the principal value of the following: `sin^-1 (1/2)`
Find the principal value of the following: tan- 1( - √3)
Find the principal value of the following: sin-1 `(1/sqrt(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)`
Evaluate cot(tan−1(2x) + cot−1(2x))
Find the principal value of the following:
tan-1 (-1)
Find the principal value of the following:
cosec-1 (2)
Solve `tan^-1 2x + tan^-1 3x = pi/4`
Prove that `tan^-1 (m/n) - tan^-1 ((m - n)/(m + n)) = pi/4`
A man standing directly opposite to one side of a road of width x meter views a circular shaped traffic green signal of diameter ‘a’ meter on the other side of the road. The bottom of the green signal Is ‘b’ meter height from the horizontal level of viewer’s eye. If ‘a’ denotes the angle subtended by the diameter of the green signal at the viewer’s eye, then prove that α = `tan^-1 (("a" + "b")/x) - tan^-1 ("b"/x)`
The value of cot `(tan^-1 2x + cot^-1 2x)` is ______
In Δ ABC, with the usual notations, if sin B sin C = `"bc"/"a"^2`, then the triangle is ______.
The value of cot (- 1110°) is equal to ______.
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 ______
The equation tan–1x – cot–1x = `(1/sqrt(3))` has ______.
Show that `2tan^-1 (-3) = (-pi)/2 + tan^-1 ((-4)/3)`
`("cos" 8° - "sin" 8°)/("cos" 8° + "sin" 8°)` is equal to ____________.
`"sin"^-1 (-1/2)`
`"cos"^-1 1/2 + 2 "sin"^-1 1/2` is equal to ____________.
If 6sin-1 (x2 – 6x + 8.5) = `pi`, then x is equal to ____________.
`2 "tan"^-1 ("cos x") = "tan"^-1 (2 "cosec x")`
The number of solutions of sin–1x + sin–1(1 – x) = cos–1x is
Domain and Rariges of cos–1 is:-
What will be the principal value of `sin^-1(-1/2)`?
Values of tan–1 – sec–1(–2) is equal to
`sin(tan^-1x), |x| < 1` is equal to
Value of `sin(pi/3 - sin^1 (- 1/2))` is equal to
What is the values of `cos^-1 (cos (7pi)/6)`
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)`.
Find the value of `sin(2cos^-1 sqrt(5)/3)`.
