Advertisements
Advertisements
प्रश्न
Find the principal value of the following:
`cot^-1(sqrt3)`
Advertisements
उत्तर
Let `cot^-1(sqrt3)=y`
Then,
`coty=sqrt3`
We know that the range of the principal value branch is (0, π).
Thus,
`coty-sqrt3=cot(pi/6)`
`=>y=pi/6in(0,pi)`
Hence, the principal value of `cot^-1(sqrt3) is pi/6.`
APPEARS IN
संबंधित प्रश्न
The principal solution of `cos^-1(-1/2)` is :
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 value of `tan^(-1) sqrt3 - cot^(-1) (-sqrt3)`
if `tan^(-1) a + tan^(-1) b + tan^(-1) x = pi`, prove that a + b + c = abc
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(2cos (2pi)/3)`
Find the principal value of the following:
`sec^-1(2)`
Find the principal value of the following:
`sec^-1(2sin (3pi)/4)`
Find the principal value of the following:
`cosec^-1(-sqrt2)`
Find the principal value of the following:
`\text(cosec)^-1(2/sqrt3)`
For the principal value, evaluate the following:
`sin^-1[cos{2\text(cosec)^-1(-2)}]`
Find the principal value of the following:
`cot^-1(-1/sqrt3)`
Show that `"sin"^-1(5/13) + "cos"^-1(3/5) = "tan"^-1(63/16)`
Solve for x, if:
tan (cos-1x) = `2/sqrt5`
Find the principal value of cos–1x, for x = `sqrt(3)/2`.
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)`
Find the values of x which satisfy the equation sin–1x + sin–1(1 – x) = cos–1x.
Which of the following corresponds to the principal value branch of tan–1?
The value of tan2 (sec–12) + cot2 (cosec–13) is ______.
Find the value of `tan^-1 (tan (5pi)/6) +cos^-1(cos (13pi)/6)`
Find the value of `tan^-1 (tan (2pi)/3)`
Find the value of `4tan^-1 1/5 - tan^-1 1/239`
Which of the following is the principal value branch of cos–1x?
Which of the following is the principal value branch of cosec–1x?
The value of `sin^-1 [cos((33pi)/5)]` is ______.
The value of the expression `2 sec^-1 2 + sin^-1 (1/2)` is ______.
The principal value of `cos^-1 (- 1/2)` is ______.
The value of `cos^-1 (cos (14pi)/3)` is ______.
The value of expression `tan((sin^-1x + cos^-1x)/2)`, when x = `sqrt(3)/2` is ______.
The result `tan^1x - tan^-1y = tan^-1 ((x - y)/(1 + xy))` is true when value of xy is ______.
The value of the expression (cos–1x)2 is equal to sec2x.
Which of the following is the principal value branch of `"cos"^-1 "x"`
What is the principal value of `cot^-1 ((-1)/sqrt(3))`?
