Advertisements
Advertisements
Question
Evaluate cot(tan−1(2x) + cot−1(2x))
Solution
cot(tan−1(2x) + cot−1(2x)) = `cot (pi/2)`
= 0 .......`[∵ tan^-1x + cot^-1 x = pi/2]`
RELATED QUESTIONS
If `tan^-1((x-1)/(x-2))+cot^-1((x+2)/(x+1))=pi/4; `
Find the principal value of `cos^(-1) (sqrt3/2)`
Find the principal value of `cos^(-1) (-1/2)`
Find the principal value of `cos^(-1) (-1/sqrt2)`
Find the principal value of `cosec^(-1)(-sqrt2)`
Find the value of the following:
`tan^(-1)(1) + cos^(-1) (-1/2) + sin^(-1) (-1/2)`
Find the value of the following:
`cos^(-1) (1/2) + 2 sin^(-1)(1/2)`
Find the value of the following:
If sin−1 x = y, then
Find the value of the following:
`cos^(-1) (cos (13pi)/6)`
Find the domain of the following function:
`f(x)=sin^-1x+sin^-1 2x`
If `sin^-1 x + sin^-1 y+sin^-1 z+sin^-1 t=2pi` , then find the value of x2 + y2 + z2 + t2
Evaluate the following:
`tan^-1(-1/sqrt3)+tan^-1(-sqrt3)+tan^-1(sin(-pi/2))`
Evaluate the following:
`tan^-1(tan (5pi)/6)+cos^-1{cos((13pi)/6)}`
Find the set of values of `cosec^-1(sqrt3/2)`
Evaluate the following:
`cot^-1 1/sqrt3-\text(cosec)^-1(-2)+sec^-1(2/sqrt3)`
Evaluate the following:
`\text(cosec)^-1(-2/sqrt3)+2cot^-1(-1)`
In ΔABC, if a = 18, b = 24, c = 30 then find the values of cosA
In ΔABC, if a = 18, b = 24, c = 30 then find the values of tan `A/2`
In ΔABC prove that `sin "A"/(2). sin "B"/(2). sin "C"/(2) = ["A(ΔABC)"]^2/"abcs"`
Find the principal value of the following: cosec- 1(2)
Evaluate the following:
`tan^-1 sqrt(3) - sec^-1 (-2)`
Evaluate the following:
`"cosec"^-1(-sqrt(2)) + cot^-1(sqrt(3))`
Prove the following:
`sin^-1(-1/2) + cos^-1(-sqrt(3)/2) = cos^-1(-1/2)`
Prove the following:
`tan^-1(1/2) + tan^-1(1/3) = pi/(4)`
Prove the following:
`2tan^-1(1/3) = tan^-1(3/4)`
In ΔABC, prove the following:
`(cos A)/a + (cos B)/b + (cos C)/c = (a^2 + b^2 + c^2)/(2abc)`
Prove that `2 tan^-1 (3/4) = tan^-1(24/7)`
Find the value of `cos^-1 (1/2) + tan^-1 (1/sqrt(3))`
If tan−1x + tan−1y + tan−1z = π, then show that `1/(xy) + 1/(yz) + 1/(zx)` = 1
Prove that `2 tan^-1 (1/8) + tan^-1 (1/7) + 2tan^-1 (1/5) = pi/4`
Find the principal value of the following:
`sec^-1 (-sqrt2)`
Prove that:
`tan^-1 (4/3) + tan^-1 (1/7) = pi/4`
Evaluate:
`cos[tan^-1 (3/4)]`
Evaluate: `cos (sin^-1 (4/5) + sin^-1 (12/13))`
Find the principal value of cosec–1(– 1)
Find the principal value of `sec^-1 (- sqrt(2))`
lf `sqrt3costheta + sintheta = sqrt2`, then the general value of θ is ______
In ΔABC, tan`A/2 = 5/6` and tan`C/2 = 2/5`, then ______
In Δ ABC, with the usual notations, if sin B sin C = `"bc"/"a"^2`, then the triangle is ______.
If `sin^-1 3/5 + cos^-1 12/13 = sin^-1 P`, then P is equal to ______
If sin `(sin^-1 1/3 + cos^-1 x) = 1`, then the value of x is ______.
`tan[2tan^-1 (1/3) - pi/4]` = ______.
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 ______
`(sin^-1(-1/2) + tan^-1(-1/sqrt(3)))/(sec^-1 (-2/sqrt(3)) + cos^-1(1/sqrt(2))` = ______.
The value of `sin^-1(cos (53pi)/5)` is ______
The domain of the function y = sin–1 (– x2) is ______.
The domain of y = cos–1(x2 – 4) is ______.
Prove that `cot(pi/4 - 2cot^-1 3)` = 7
If 2 tan–1(cos θ) = tan–1(2 cosec θ), then show that θ = π 4, where n is any integer.
Show that `cos(2tan^-1 1/7) = sin(4tan^-1 1/3)`
Solve the following equation `cos(tan^-1x) = sin(cot^-1 3/4)`
Prove that `tan^-1 1/4 + tan^-1 2/9 = sin^-1 1/sqrt(5)`
All trigonometric functions have inverse over their respective domains.
When `"x" = "x"/2`, then tan x is ____________.
`"sin" 265° - "cos" 265°` is ____________.
`"sin"^-1 (1/sqrt2)`
`"cos"^-1 1/2 + 2 "sin"^-1 1/2` is equal to ____________.
If tan-1 (x – 1) + tan-1 x + tan-1 (x + 1) = tan-1 3x, then the values of x are ____________.
If 6sin-1 (x2 – 6x + 8.5) = `pi`, then x is equal to ____________.
`"sin"^-1 (1 - "x") - 2 "sin"^-1 "x" = pi/2`
The value of `"cos"^-1 ("cos" ((33 pi)/5))` is ____________.
`"cos"^-1 ["cos" (2 "cot"^-1 (sqrt2 - 1))] =` ____________.
Find the value of sec2 (tan-1 2) + cosec2 (cot-1 3) ____________.
If tan-1 x – tan-1 y = tan-1 A, then A is equal to ____________.
The equation of the tangent to the curve given by x = a sin3t, y = bcos3t at a point where t = `pi/2` is
If A = `[(cosx, sinx),(-sinx, cosx)]`, then A1 A–1 is
What is the value of `sin^-1(sin (3pi)/4)`?
What will be the principal value of `sin^-1(-1/2)`?
`2tan^-1 (cos x) = tan^-1 (2"cosec" x)`, then 'x' will be equal to
If f(x) = x5 + 2x – 3, then (f–1)1 (–3) = ______.
If f'(x) = x–1, then find f(x)
Assertion (A): The domain of the function sec–12x is `(-∞, - 1/2] ∪ pi/2, ∞)`
Reason (R): sec–1(–2) = `- pi/4`
`lim_(n→∞)tan{sum_(r = 1)^n tan^-1(1/(1 + r + r^2))}` is equal to ______.
If θ = `sin^-1((2x)/(1 + x^2)) + cos^-1((1 - x^2)/(1 + x^2))`, for `x ≥ 3/2` then the absolute value of `((cosθ + tanθ + 4)/secθ)` is ______.
Consider f(x) = sin–1[2x] + cos–1([x] – 1) (where [.] denotes greatest integer function.) If domain of f(x) is [a, b) and the range of f(x) is {c, d} then `a + b + (2d)/c` is equal to ______. (where c < d)
Number of values of x satisfying the system of equations `sin^-1sqrt(2 + e^(-2x) - 2e^-x) + sec^-1sqrt(1 - x^2 + x^4) = π/2` and `5^(1+tan^-1x)` = 4 + [cos–1x] is ______ (where [.] denotes greatest integer function)
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)`.
If 2 tan–1 (cosx) = tan–1 (2 cosec x), then sin x + cos x is equal to ______.
If y = `tan^-1 (sqrt(1 + x^2) - sqrt(1 - x^2))/(sqrt(1 + x^2) + sqrt(1 - x^2))`, then `dy/dx` is equal to ______.
Find the value of `sin(2cos^-1 sqrt(5)/3)`.
Find the value of `tan^-1(x/y) + tan^-1((y - x)/(y + x))`