Advertisements
Advertisements
प्रश्न
The domain of sin–1 2x is ______.
पर्याय
[0, 1]
[– 1, 1]
`[-1/2, 1/2]`
[–2, 2]
Advertisements
उत्तर
The domain of sin–1 2x is `[-1/2, 1/2]`.
Explanation:
Let sin–12x = θ
So that 2x = sin θ.
Now – 1 ≤ sin θ ≤ 1
i.e.,– 1 ≤ 2x ≤ 1
Which gives `-1/2 ≤ x ≤ 1/2`.
APPEARS IN
संबंधित प्रश्न
The principal solution of the equation cot x=`-sqrt 3 ` is
Prove that `sin^(-1) (3/5) + cos^(-1) (12/13) = sin^(-1) (56/65)`
Find the value of `tan^(-1) sqrt3 - cot^(-1) (-sqrt3)`
Solve `3tan^(-1)x + cot^(-1) x = pi`
Find the principal value of the following:
`sin^-1(cos (2pi)/3)`
Find the principal value of the following:
`sin^-1(tan (5pi)/4)`
Find the principal value of the following:
`tan^-1(1/sqrt3)`
Find the principal value of the following:
`tan^-1(2cos (2pi)/3)`
For the principal value, evaluate of the following:
`tan^-1{2sin(4cos^-1 sqrt3/2)}`
Find the principal value of the following:
`sec^-1(-sqrt2)`
Find the principal value of the following:
`sec^-1(2)`
For the principal value, evaluate the following:
`tan^-1sqrt3-sec^-1(-2)`
Find the principal value of the following:
cosec-1(-2)
Find the principal value of the following:
`cot^-1(sqrt3)`
Show that `"sin"^-1(5/13) + "cos"^-1(3/5) = "tan"^-1(63/16)`
If `sin^-1"x" + tan^-1"x" = pi/2`, prove that `2"x"^2 + 1 = sqrt5`
Find the value of `sec(tan^-1 y/2)`
The value of `sin^-1 (cos((43pi)/5))` is ______.
The principal value of `sin^-1 ((-sqrt(3))/2)` is ______.
The value of `tan(cos^-1 3/5 + tan^-1 1/4)` is ______.
Find the value of the expression `sin(2tan^-1 1/3) + cos(tan^-1 2sqrt(2))`
The value of the expression `2 sec^-1 2 + sin^-1 (1/2)` is ______.
The principal value of `cos^-1 (- 1/2)` is ______.
The value of `cos^-1 (cos (14pi)/3)` is ______.
The result `tan^1x - tan^-1y = tan^-1 ((x - y)/(1 + xy))` is true when value of xy is ______.
The value of the expression (cos–1x)2 is equal to sec2x.
The domain of trigonometric functions can be restricted to any one of their branch (not necessarily principal value) in order to obtain their inverse functions.
The least numerical value, either positive or negative of angle θ is called principal value of the inverse trigonometric function.
The principal value of `sin^-1 [cos(sin^-1 1/2)]` is `pi/3`.
If `5 sin theta = 3 "then", (sec theta + tan theta)/(sec theta - tan theta)` is equal to ____________.
The general solution of the equation `"cot" theta - "tan" theta = "sec" theta` is ____________ where `(n in I).`
If `"tan"^-1 "x" + "tan"^-1"y + tan"^-1 "z" = pi/2, "x,y,x" > 0,` then the value of xy+yz+zx is ____________.
Which of the following is the principal value branch of `"cos"^-1 "x"`
What is the value of `tan^-1(1) cos^-1(- 1/2) + sin^-1(- 1/2)`
Assertion (A): Maximum value of (cos–1 x)2 is π2.
Reason (R): Range of the principal value branch of cos–1 x is `[(-π)/2, π/2]`.
Evaluate `sin^-1 (sin (3π)/4) + cos^-1 (cos π) + tan^-1 (1)`.
