Advertisements
Advertisements
Question
If |x| ≤ 1, then `2 tan^-1x + sin^-1 ((2x)/(1 + x^2))` is equal to ______.
Options
`4 tan^-1x`
0
`pi/2`
π
Advertisements
Solution
If |x| ≤ 1, then `2 tan^-1x + sin^-1 ((2x)/(1 + x^2))` is equal to `4 tan^-1x`.
Explanation:
Here, we have `2 tan^-1x + sin^-1 ((2x)/(1 + x^2))`
= `2tan^-1x + 2tan^-1x` ....`[because 2 tan^-1x = sin^-1 (2x)/(1 + x^2)]`
= 4 tan–1x
APPEARS IN
RELATED QUESTIONS
Prove that `2tan^(-1)(1/5)+sec^(-1)((5sqrt2)/7)+2tan^(-1)(1/8)=pi/4`
Prove that `tan^(-1)((6x-8x^3)/(1-12x^2))-tan^(-1)((4x)/(1-4x^2))=tan^(-1)2x;|2x|<1/sqrt3`
Prove `tan^(-1) 2/11 + tan^(-1) 7/24 = tan^(-1) 1/2`
Write the function in the simplest form: `tan^(-1) ((cos x - sin x)/(cos x + sin x)) `,` 0 < x < pi`
Find the value of the following:
`tan 1/2 [sin^(-1) (2x)/(1 + x^2) + cos^(-1) (1 - y^2)/(1 + y^2)], |x| < 1, y > 0 and xy < 1`
Find the value of the given expression.
`sin^(-1) (sin (2pi)/3)`
Find the value of the given expression.
`tan^(-1) (tan (3pi)/4)`
Prove that `cos^(-1) 12/13 + sin^(-1) 3/5 = sin^(-1) 56/65`.
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)`.
Find: ∫ sin x · log cos x dx
Find the value of the expression in terms of x, with the help of a reference triangle
`tan(sin^-1(x + 1/2))`
If tan–1x + tan–1y + tan–1z = π, show that x + y + z = xyz
Prove that `tan^-1x + tan^-1 (2x)/(1 - x^2) = tan^-1 (3x - x^3)/(1 - 3x^2), |x| < 1/sqrt(3)`
Choose the correct alternative:
`tan^-1 (1/4) + tan^-1 (2/9)` is equal to
Evaluate tan (tan–1(– 4)).
Prove that cot–17 + cot–18 + cot–118 = cot–13
If α ≤ 2 sin–1x + cos–1x ≤ β, then ______.
Prove that `sin^-1 8/17 + sin^-1 3/5 = sin^-1 7/85`
Show that `tan(1/2 sin^-1 3/4) = (4 - sqrt(7))/3` and justify why the other value `(4 + sqrt(7))/3` is ignored?
If 3 tan–1x + cot–1x = π, then x equals ______.
If cos–1α + cos–1β + cos–1γ = 3π, then α(β + γ) + β(γ + α) + γ(α + β) equals ______.
The number of real solutions of the equation `sqrt(1 + cos 2x) = sqrt(2) cos^-1 (cos x)` in `[pi/2, pi]` is ______.
The minimum value of sinx - cosx is ____________.
If `"sec" theta = "x" + 1/(4 "x"), "x" in "R, x" ne 0,`then the value of `"sec" theta + "tan" theta` is ____________.
The value of `"tan"^ -1 (3/4) + "tan"^-1 (1/7)` is ____________.
If `"tan"^-1 ("cot" theta) = 2theta, "then" theta` is equal to ____________.
`"tan"^-1 1 + "cos"^-1 ((-1)/2) + "sin"^-1 ((-1)/2)`
If `"cot"^-1 (sqrt"cos" alpha) - "tan"^-1 (sqrt"cos" alpha) = "x",` the sinx is equal to ____________.
`"sin" {2 "cos"^-1 ((-3)/5)}` is equal to ____________.
Simplest form of `tan^-1 ((sqrt(1 + cos "x") + sqrt(1 - cos "x"))/(sqrt(1 + cos "x") - sqrt(1 - cos "x")))`, `π < "x" < (3π)/2` is:
`"tan"^-1 1 + "cos"^-1 ((-1)/2) + "sin"^-1 ((-1)/2)`
`tan^-1 1/2 + tan^-1 2/11` is equal to
If `cos^-1(2/(3x)) + cos^-1(3/(4x)) = π/2(x > 3/4)`, then x 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
Write the following function in the simplest form:
`tan^-1 ((cos x - sin x)/(cos x + sin x)), (-pi)/4 < x < (3 pi)/4`
`tan^-1 sqrt3 - cot^-1 (- sqrt3)` is equal to ______.
Solve for x: `sin^-1(x/2) + cos^-1x = π/6`
