Advertisements
Advertisements
प्रश्न
Find the principal value of `cot^-1 ((-1)/sqrt(3))`
Advertisements
उत्तर
Let y = `cot^-1 ((-1)/sqrt(3))`
Since, cot–1(– x) = π – cot–1x
∴ y = `π - cot^-1 (1/sqrt(3))`
⇒ y = `π - π/3` ......`(∵ cot π/3 = 1/sqrt(3))`
⇒ y = `(2π)/3`
Since, range of cot–1 is (0, π)
Hence, principal value is `(2π)/3`.
APPEARS IN
संबंधित प्रश्न
Find the principal value of the following:
`cos^(-1) (sqrt3/2)`
Find the principal value of the following:
`cot^(-1) (sqrt3)`
Find the principal value of the following:
`"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)`
Evaluate the following:
`tan^-1 1+cos^-1 (-1/2)+sin^-1(-1/2)`
Evaluate the following:
`cot^-1 1/sqrt3-\text(cosec)^-1(-2)+sec^-1(2/sqrt3)`
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 cosA
In ΔABC prove that `(b + c - a) tan "A"/(2) = (c + a - b)tan "B"/(2) = (a + b - c)tan "C"/(2)`.
Find the principal value of the following: tan-1(– 1)
Evaluate the following:
`cos^-1(1/2) + 2sin^-1(1/2)`
Prove the following:
`sin^-1(1/sqrt(2)) -3sin^-1(sqrt(3)/2) = -(3π)/(4)`
Prove the following:
`tan^-1[sqrt((1 - cosθ)/(1 + cosθ))] = θ/(2)`, if θ ∈ (– π, π).
In ΔABC, prove the following:
`(cos A)/a + (cos B)/b + (cos C)/c = (a^2 + b^2 + c^2)/(2abc)`
If `sin(sin^-1(1/5) + cos^-1(x))` = 1, then x = ______
Evaluate cot(tan−1(2x) + cot−1(2x))
Evaluate:
`sin[cos^-1 (3/5)]`
Find the principal value of the following:
tan-1 (-1)
Find the principal value of the following:
cosec-1 (2)
Prove that:
`tan^-1 (4/3) + tan^-1 (1/7) = pi/4`
Show that `tan^-1 (1/2) + tan^-1 (2/11) = tan^-1 (3/4)`
Express `tan^-1 [(cos x)/(1 - sin x)], - pi/2 < x < (3pi)/2` in the simplest form.
Find the principal value of `sec^-1 (- sqrt(2))`
In ΔABC, tan`A/2 = 5/6` and tan`C/2 = 2/5`, then ______
sin[3 sin-1 (0.4)] = ______.
The principal value of `tan^{-1(sqrt3)}` is ______
Prove that `cot(pi/4 - 2cot^-1 3)` = 7
Show that `2tan^-1 (-3) = (-pi)/2 + tan^-1 ((-4)/3)`
Show that `cos(2tan^-1 1/7) = sin(4tan^-1 1/3)`
Solve the following equation `cos(tan^-1x) = sin(cot^-1 3/4)`
If `"x + y" = "x"/4` then (1+ tanx)(1 + tany) is equal to ____________.
`"tan"^-1 (sqrt3)`
`2 "tan"^-1 ("cos x") = "tan"^-1 (2 "cosec x")`
`"tan"(pi/4 + 1/2 "cos"^-1 "x") + "tan" (pi/4 - 1/2 "cos"^-1 "x") =` ____________.
`"cos"^-1 ("cos" ((7pi)/6))` is equal to ____________.
sin 6θ + sin 4θ + sin 2θ = 0, then θ =
`sin(tan^-1x), |x| < 1` is equal to
Value of `sin(pi/3 - sin^1 (- 1/2))` is equal to
If f(x) = x5 + 2x – 3, then (f–1)1 (–3) = ______.
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)`.
Derivative of `tan^-1(x/sqrt(1 - x^2))` with respect sin–1(3x – 4x3) is ______.
Prove that:
tan–1x + tan–1y = `π + tan^-1((x + y)/(1 - xy))`, provided x > 0, y > 0, xy > 1
Find the value of `sin(2cos^-1 sqrt(5)/3)`.
Solve for x:
5tan–1x + 3cot–1x = 2π
