Advertisements
Advertisements
प्रश्न
Find the value of `tan^(-1) sqrt3 - cot^(-1) (-sqrt3)`
उत्तर
`tan^(-1) (sqrt3) -cot^(-1) (-sqrt3)`
`= tan^(-1) {tan (pi/3)} - cot^(-1) (cot (5pi)/6)` [∵ Range of `tan^(-1) is (-pi/2, pi/2); pi/3 in (-pi/2, pi/2)`
and range of `cot^(-1) is [0, pi]; (5pi)/6 in [0,pi]]`
`= pi/3 - (5pi)/6`
`= -pi/2`
APPEARS IN
संबंधित प्रश्न
The principal solution of `cos^-1(-1/2)` is :
Find the principal value of the following:
`sin^-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)`
Find the principal value of the following:
cosec-1(-2)
Find the principal value of the following:
`cosec^-1(2cos (2pi)/3)`
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(-1/sqrt3)`
Find the principal value of the following:
`cot^-1(tan (3pi)/4)`
Find the principal value of cos–1x, for x = `sqrt(3)/2`.
Find the value of `cos^-1(cos (13pi)/6)`.
Find the value of `tan^-1 (tan (9pi)/8)`.
Find value of tan (cos–1x) and hence evaluate `tan(cos^-1 8/17)`
The principal value branch of sec–1 is ______.
The principal value of `sin^-1 ((-sqrt(3))/2)` is ______.
The greatest and least values of (sin–1x)2 + (cos–1x)2 are respectively ______.
Find the value of `tan^-1 (tan (5pi)/6) +cos^-1(cos (13pi)/6)`
The domain of the function cos–1(2x – 1) is ______.
If tan–1x + tan–1y = `(4pi)/5`, then cot–1x + cot–1y equals ______.
The set of values of `sec^-1 (1/2)` is ______.
The principal value of `sin^-1 [cos(sin^-1 1/2)]` is `pi/3`.
The general solution of the equation `"cot" theta - "tan" theta = "sec" theta` is ____________ where `(n in I).`
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 ____________.
Which of the following is the principal value branch of `"cos"^-1 "x"`
What is the value of x so that the seven-digit number 8439 × 53 is divisible by 99?
