Advertisements
Advertisements
प्रश्न
Find the principal value of the following:
`cosec^-1(2cos (2pi)/3)`
उत्तर
Let `cosec^-1(2cos (2pi)/3)=y`
Then,
`cosec y=2cos (2pi)/3`
We know that the range of the principal value branch is `[-pi/2,pi/2]-{0}.`
Thus,
`cosec y =2cos (2pi)/3=2xx(-1)/2=-1=cosec(-pi/2).`
`=>y=-pi/2in[-pi/2,pi/2],y!=0`
Hence, the principal value of `cosec^-1(2cos (2pi)/3) is -pi/2.`
APPEARS IN
संबंधित प्रश्न
Find the principal value of the following:
`sin^-1(-sqrt3/2)`
Find the principal value of the following:
`sin^-1((sqrt3-1)/(2sqrt2))`
For the principal value, evaluate of the following:
`sin^-1(-sqrt3/2)+cos^-1(sqrt3/2)`
Find the principal value of the following:
`tan^-1(1/sqrt3)`
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:
`sec^-1(2tan (3pi)/4)`
For the principal value, evaluate the following:
`tan^-1sqrt3-sec^-1(-2)`
Find the principal value of the following:
cosec-1(-2)
For the principal value, evaluate the following:
`cosec^-1(2tan (11pi)/6)`
Find the principal value of the following:
`cot^-1(tan (3pi)/4)`
Show that `"sin"^-1(5/13) + "cos"^-1(3/5) = "tan"^-1(63/16)`
if sec-1 x = cosec-1 v. show that `1/x^2 + 1/y^2 = 1`
If `sin^-1"x" + tan^-1"x" = pi/2`, prove that `2"x"^2 + 1 = sqrt5`
Find the value of `cos^-1(cos (13pi)/6)`.
Find the value of `sec(tan^-1 y/2)`
Find value of tan (cos–1x) and hence evaluate `tan(cos^-1 8/17)`
Find the value of `sin[2cot^-1 ((-5)/12)]`
One branch of cos–1 other than the principal value branch corresponds to ______.
The value of the expression sin [cot–1 (cos (tan–11))] is ______.
Which of the following is the principal value branch of cosec–1x?
The value of sin (2 tan–1(0.75)) is equal to ______.
If tan–1x + tan–1y = `(4pi)/5`, then cot–1x + cot–1y equals ______.
The value of `sin^-1 (sin (3pi)/5)` is ______.
The principal value of `tan^-1 sqrt(3)` 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 domain of trigonometric functions can be restricted to any one of their branch (not necessarily principal value) in order to obtain their inverse functions.
The period of the function f(x) = cos4x + tan3x is ____________.
If `"tan"^-1 ("a"/"x") + "tan"^-1 ("b"/"x") = pi/2,` then x is equal to ____________.
`"sec" {"tan"^-1 (-"y"/3)}` 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?
What is the principle value of `sin^-1 (1/sqrt(2))`?
