Advertisements
Advertisements
Question
Find the principal value of `cot^(-1) (sqrt3)`
Solution
Let `cot^(-1)(sqrt3) = y` Then `cot y = sqrt3 = cot (pi/6)`
We know that the range of the principal value branch of cot−1 is (0,π)
`"Then"cot (pi/6) = sqrt3`
Where `pi/6 ∈ (0, pi)`
Therefore, the principal value of `cot^(-1) (sqrt3) " is " pi/6.`
APPEARS IN
RELATED QUESTIONS
Find the principal values of `sin^(-1) (-1/2)`
Find the principal value of cosec−1 (2)
Find the value of the following:
`tan^(-1) (tan (7x)/6)`
Prove that:
`tan^-1 ((sqrt(1 + x) - sqrt(1 - x))/(sqrt(1 + x) + sqrt(1 - x))) = pi/4 - 1/2 cos^-1 x`, for `- 1/sqrt2 <= x <= 1`
[Hint: put x = cos 2θ]
Find the principal value of `sin^-1(1/sqrt2)`
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))`
Find the principal value of the following: tan- 1( - √3)
Find the principal value of the following: sin-1 `(1/sqrt(2))`
Evaluate the following:
`tan^-1(1) + cos^-1(1/2) + sin^-1(1/2)`
Prove the following:
`sin^-1(1/sqrt(2)) -3sin^-1(sqrt(3)/2) = -(3π)/(4)`
Prove the following:
`sin^-1(-1/2) + cos^-1(-sqrt(3)/2) = cos^-1(-1/2)`
Prove the following:
`cos^-1(3/5) + cos^-1(4/5) = pi/(2)`
Prove the following:
`2tan^-1(1/3) = tan^-1(3/4)`
Prove the following:
`tan^-1[sqrt((1 - cosθ)/(1 + cosθ))] = θ/(2)`, if θ ∈ (– π, π).
Evaluate cot(tan−1(2x) + cot−1(2x))
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:
2 tan-1 (x) = `sin^-1 ((2x)/(1 + x^2))`
Evaluate: `cos (sin^-1 (4/5) + sin^-1 (12/13))`
Prove that `tan^-1 (m/n) - tan^-1 ((m - n)/(m + n)) = pi/4`
Show that `sin^-1 (- 3/5) - sin^-1 (- 8/17) = cos^-1 (84/85)`
In ΔABC, tan`A/2 = 5/6` and tan`C/2 = 2/5`, then ______
The principle solutions of equation tan θ = -1 are ______
Which of the following function has period 2?
If sin `(sin^-1 1/3 + cos^-1 x) = 1`, then the value of x is ______.
`"tan"^-1 (sqrt3)`
Find the value of sec2 (tan-1 2) + cosec2 (cot-1 3) ____________.
The inverse of `f(x) = sqrt(3x^2 - 4x + 5)` is
What is the principal value of cosec–1(2).
cos–1(cos10) is equal to ______.
The value of cos (2cos–1 x + sin–1 x) at x = `1/5` is ______.
Derivative of `tan^-1(x/sqrt(1 - x^2))` with respect sin–1(3x – 4x3) is ______.
If 2 tan–1 (cosx) = tan–1 (2 cosec x), then sin x + cos x is equal to ______.
Find the value of `cos(x/2)`, if tan x = `5/12` and x lies in third quadrant.
Find the value of `tan^-1(x/y) + tan^-1((y - x)/(y + x))`
