Advertisements
Advertisements
प्रश्न
Find the principal value of the following:
`cot^-1(-sqrt3)`
Advertisements
उत्तर
Let `cot^-1(-sqrt3)` = y
Then,
cot y = `-sqrt3`
We know that the range of the principal value branch is (0, π)
Thus,
cot y = `-sqrt3 = cot((5pi)/6)`
`\implies` y = `(5pi)/6in(0, pi)`
Hence, the principal value of `cot^-1(-sqrt3)` is `(5pi)/6.`
APPEARS IN
संबंधित प्रश्न
Write the principal value of `tan^(-1)+cos^(-1)(-1/2)`
Prove that `sin^(-1) (3/5) + cos^(-1) (12/13) = sin^(-1) (56/65)`
Find the principal value of the following:
`sin^-1(cos (2pi)/3)`
For the principal value, evaluate of the following:
`cos^-1 1/2 + 2 sin^-1 (1/2)`
For the principal value, evaluate of the following:
`sin^-1(-1/2)+2cos^-1(-sqrt3/2)`
Find the principal value of the following:
`tan^-1(1/sqrt3)`
Find the principal value of the following:
`sec^-1(2sin (3pi)/4)`
For the principal value, evaluate the following:
`tan^-1sqrt3-sec^-1(-2)`
Find the principal value of the following:
`cosec^-1(-sqrt2)`
Find the principal value of the following:
cosec-1(-2)
Find the principal value of the following:
`\text(cosec)^-1(2/sqrt3)`
For the principal value, evaluate the following:
`sin^-1(-sqrt3/2)+\text{cosec}^-1(-2/sqrt3)`
For the principal value, evaluate the following:
`sec^-1(sqrt2)+2\text{cosec}^-1(-sqrt2)`
Find the principal value of the following:
`cot^-1(tan (3pi)/4)`
Solve for x, if:
tan (cos-1x) = `2/sqrt5`
Find the value of `tan^-1 (tan (9pi)/8)`.
Prove that tan(cot–1x) = cot(tan–1x). State with reason whether the equality is valid for all values of x.
Find the value of `sec(tan^-1 y/2)`
The principal value of the expression cos–1[cos (– 680°)] is ______.
The value of cot (sin–1x) is ______.
Let θ = sin–1 (sin (– 600°), then value of θ is ______.
The value of the expression sin [cot–1 (cos (tan–11))] is ______.
Find the value of `tan^-1 (tan (5pi)/6) +cos^-1(cos (13pi)/6)`
Find the value of `tan^-1 (- 1/sqrt(3)) + cot^-1(1/sqrt(3)) + tan^-1(sin((-pi)/2))`
Find the value of `tan^-1 (tan (2pi)/3)`
Which of the following is the principal value branch of cos–1x?
If `cos(sin^-1 2/5 + cos^-1x)` = 0, then x is equal to ______.
The value of `sin^-1 (sin (3pi)/5)` is ______.
If `cos(tan^-1x + cot^-1 sqrt(3))` = 0, then value of x is ______.
The principal value of `tan^-1 sqrt(3)` is ______.
The minimum value of n for which `tan^-1 "n"/pi > pi/4`, n ∈ N, is valid is 5.
If `5 sin theta = 3 "then", (sec theta + tan theta)/(sec theta - tan theta)` is equal to ____________.
If sin `("sin"^-1 1/5 + "cos"^-1 "x") = 1,` then the value of x is ____________.
If `"tan"^-1 ("a"/"x") + "tan"^-1 ("b"/"x") = pi/2,` then x is equal to ____________.
