Advertisements
Advertisements
Question
Find the principal value of the following:
`cot^(-1) (sqrt3)`
Advertisements
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 domain of the following function:
`f(x)=sin^-1x^2`
Find the domain of the following function:
`f(x) = sin^-1x + sinx`
If `sin^-1 x + sin^-1 y+sin^-1 z+sin^-1 t=2pi` , then find the value of x2 + y2 + z2 + t2
Find the set of values of `cosec^-1(sqrt3/2)`
Evaluate the following:
`cot^-1{2cos(sin^-1 sqrt3/2)}`
Prove the following:
`sin^-1(1/sqrt(2)) -3sin^-1(sqrt(3)/2) = -(3π)/(4)`
Find the principal solutions of the following equation:
cot 2θ = 0.
If `sin(sin^-1(1/5) + cos^-1(x))` = 1, then x = ______
Evaluate `cos[pi/6 + cos^-1 (- sqrt(3)/2)]`
If tan−1x + tan−1y + tan−1z = π, then show that `1/(xy) + 1/(yz) + 1/(zx)` = 1
Prove that sin `[tan^-1 ((1 - x^2)/(2x)) + cos^-1 ((1 - x^2)/(1 + x^2))]` = 1
Show that `sin^-1 (- 3/5) - sin^-1 (- 8/17) = cos^-1 (84/85)`
Find the principal value of `sec^-1 (- sqrt(2))`
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 ______.
Which of the following function has period 2?
`cos(2sin^-1 3/4+cos^-1 3/4)=` ______.
`(sin^-1(-1/2) + tan^-1(-1/sqrt(3)))/(sec^-1 (-2/sqrt(3)) + cos^-1(1/sqrt(2))` = ______.
If `3tan^-1x +cot^-1x = pi`, then xis equal to ______.
Show that `2tan^-1 (-3) = (-pi)/2 + tan^-1 ((-4)/3)`
Solve the following equation `cos(tan^-1x) = sin(cot^-1 3/4)`
If sin-1 x – cos-1 x `= pi/6,` then x = ____________.
`2 "tan"^-1 ("cos x") = "tan"^-1 (2 "cosec x")`
The value of `"cos"^-1 ("cos" ((33 pi)/5))` is ____________.
3 tan-1 a is equal to ____________.
If `"x" in (- pi/2, pi/2), "then the value of tan"^-1 ("tan x"/4) + "tan"^-1 ((3 "sin" 2 "x")/(5 + 3 "cos" 2 "x"))` is ____________.
If `"cot"^-1 (sqrt"cos" alpha) - "tan"^-1 (sqrt "cos" alpha) = "x",` then sinx is equal to ____________.
Find the value, if sin–1x = y, then `->`:-
Values of tan–1 – sec–1(–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 which lie in [0, 2π] and satisfy the equation
`(cos x/4 - 2sinx) sinx + (1 + sin x/4 - 2cosx)cosx` = 0
If tan–1 (2x) + tan–1 (3x) = `π/4`, then x = ______.
The value of `cos^-1(cos(π/2)) + cos^-1(sin((2π)/2))` is ______.
Derivative of `tan^-1(x/sqrt(1 - x^2))` with respect sin–1(3x – 4x3) is ______.
`sin[π/3 + sin^-1 (1/2)]` is equal to ______.
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)`.
