Advertisements
Advertisements
प्रश्न
If y = `2 tan^-1x + sin^-1 ((2x)/(1 + x^2))` for all x, then ______ < y < ______.
Advertisements
उत्तर
If y = `2 tan^-1x + sin^-1 ((2x)/(1 + x^2))` for all x, then – 2π < y < 2π.
Explanation:
y = `2 tan^-1x + sin^-1 ((2x)/(1 + x^2))`
⇒ y = `2 tan^-1x + 2 tan^-1x`1
⇒ y = `4 tan^-1x` ......`[because sin^1 ((x)/(1 +x^2)) = 2tan^-1x]`
Now `(-pi)/2 < tan^-1x < pi/2`
⇒ `-4 xx pi/2 < 4 tan^-1x < 4 xx pi/2`
⇒ – 2π < y < 2π.
APPEARS IN
संबंधित प्रश्न
Prove that:
`tan^(-1)""1/5+tan^(-1)""1/7+tan^(-1)""1/3+tan^(-1)""1/8=pi/4`
Write the following function in the simplest form:
`tan^(-1) x/(sqrt(a^2 - x^2))`, |x| < a
Write the following function in the simplest form:
`tan^(-1) ((3a^2 x - x^3)/(a^3 - 3ax^2)), a > 0; (-a)/sqrt3 < x < a/sqrt3`
Find the value of the following:
`tan^-1 [2 cos (2 sin^-1 1/2)]`
Find the value of the given expression.
`tan(sin^(-1) 3/5 + cot^(-1) 3/2)`
Prove that:
`sin^(-1) 8/17 + sin^(-1) 3/5 = tan^(-1) 77/36`
Prove `(9pi)/8 - 9/4 sin^(-1) 1/3 = 9/4 sin^(-1) (2sqrt2)/3`
Solve `tan^(-1) - tan^(-1) (x - y)/(x+y)` is equal to
(A) `pi/2`
(B). `pi/3`
(C) `pi/4`
(D) `(-3pi)/4`
If tan-1 x - cot-1 x = tan-1 `(1/sqrt(3)),`x> 0 then find the value of x and hence find the value of sec-1 `(2/x)`.
Solve: tan-1 4 x + tan-1 6x `= π/(4)`.
Find the value of the expression in terms of x, with the help of a reference triangle
sin (cos–1(1 – x))
Find the value of the expression in terms of x, with the help of a reference triangle
cos (tan–1 (3x – 1))
Find the value of `cot[sin^-1 3/5 + sin^-1 4/5]`
Simplify: `tan^-1 x/y - tan^-1 (x - y)/(x + y)`
Solve: `2tan^-1 (cos x) = tan^-1 (2"cosec" x)`
Choose the correct alternative:
`sin^-1 3/5 - cos^-1 13/13 + sec^-1 5/3 - "cosec"^-1 13/12` is equal to
Choose the correct alternative:
`sin^-1 (tan pi/4) - sin^-1 (sqrt(3/x)) = pi/6`. Then x is a root of the equation
Choose the correct alternative:
The equation tan–1x – cot–1x = `tan^-1 (1/sqrt(3))` has
Choose the correct alternative:
If `sin^-1x + cot^-1 (1/2) = pi/2`, then x is equal to
Prove that cot–17 + cot–18 + cot–118 = cot–13
Solve the equation `sin^-1 6x + sin^-1 6sqrt(3)x = - pi/2`
If cos–1α + cos–1β + cos–1γ = 3π, then α(β + γ) + β(γ + α) + γ(α + β) equals ______.
The value of `"tan"^-1 (1/2) + "tan"^-1 (1/3) + "tan"^-1 (7/8)` is ____________.
The value of `"tan"^ -1 (3/4) + "tan"^-1 (1/7)` is ____________.
`"cot" ("cosec"^-1 5/3 + "tan"^-1 2/3) =` ____________.
`"cos" (2 "tan"^-1 1/7) - "sin" (4 "sin"^-1 1/3) =` ____________.
If tan-1 2x + tan-1 3x = `pi/4,` then x is ____________.
`"cos"^-1["cos"(2"cot"^-1(sqrt2 - 1))]` = ____________.
`"tan"^-1 1 + "cos"^-1 ((-1)/2) + "sin"^-1 ((-1)/2)`
`"sin"^-1 (1/sqrt2)`
`"cos"^-1 (1/2)`
If `"sin"^-1 (1 - "x") - 2 "sin"^-1 ("x") = pi/2,` then x is equal to ____________.
If `3 "sin"^-1 ((2"x")/(1 + "x"^2)) - 4 "cos"^-1 ((1 - "x"^2)/(1 + "x"^2)) + 2 "tan"^-1 ((2"x")/(1 - "x"^2)) = pi/3` then x is equal to ____________.
`tan(2tan^-1 1/5 + sec^-1 sqrt(5)/2 + 2tan^-1 1/8)` is equal to ______.
If `tan^-1 ((x - 1)/(x + 1)) + tan^-1 ((2x - 1)/(2x + 1)) = tan^-1 (23/36)` = then prove that 24x2 – 23x – 12 = 0
The value of cosec `[sin^-1((-1)/2)] - sec[cos^-1((-1)/2)]` is equal to ______.
