Advertisements
Advertisements
प्रश्न
Find the principal value of the following:
`\text(cosec)^-1(2/sqrt3)`
उत्तर
Let `\text(cosec)^-1(2/sqrt3)=y`
Then,
`\text(cosec) y=2/sqrt3`
We know that the range of the principal value branch is `[-pi/2,pi/2]-{0}`
Thus,
`\text(cosec) y=2/sqrt3=text(cosec)(pi/3)`
`=>y=pi/3in[-pi/2,pi/2],y!=0`
Hence, the principal value of `\text(cosec)^-1(2/sqrt3) is pi/3`
APPEARS IN
संबंधित प्रश्न
Find the value of `tan^(-1) sqrt3 - cot^(-1) (-sqrt3)`
Solve `3tan^(-1)x + cot^(-1) x = pi`
if `tan^(-1) a + tan^(-1) b + tan^(-1) x = pi`, prove that a + b + c = abc
Find the principal value of the following:
`sin^-1(cos (2pi)/3)`
Find the principal value of the following:
`sin^-1(cos (3pi)/4)`
For the principal value, evaluate of the following:
`sin^-1(-sqrt3/2)+cos^-1(sqrt3/2)`
For the principal value, evaluate the following:
`sin^-1(-sqrt3/2)-2sec^-1(2tan pi/6)`
For the principal value, evaluate the following:
`sec^-1(sqrt2)+2\text{cosec}^-1(-sqrt2)`
For the principal value, evaluate the following:
`sin^-1[cos{2\text(cosec)^-1(-2)}]`
Show that `"sin"^-1(5/13) + "cos"^-1(3/5) = "tan"^-1(63/16)`
The index number by the method of aggregates for the year 2010, taking 2000 as the base year, was found to be 116. If sum of the prices in the year 2000 is ₹ 300, find the values of x and y in the data given below
| Commodity | A | B | C | D | E | F |
| Price in the year 2000 (₹) | 50 | x | 30 | 70 | 116 | 20 |
| Price in the year 2010 (₹) | 60 | 24 | y | 80 | 120 | 28 |
Find the value of `sin[2cot^-1 ((-5)/12)]`
The principal value branch of sec–1 is ______.
One branch of cos–1 other than the principal value branch corresponds to ______.
The value of cot (sin–1x) is ______.
The principal value of `sin^-1 ((-sqrt(3))/2)` is ______.
The value of `tan(cos^-1 3/5 + tan^-1 1/4)` is ______.
The value of tan2 (sec–12) + cot2 (cosec–13) is ______.
The domain of the function defined by f(x) = `sin^-1 sqrt(x- 1)` is ______.
If `cos(sin^-1 2/5 + cos^-1x)` = 0, then x is equal to ______.
The value of `cot[cos^-1 (7/25)]` is ______.
The value of `sin^-1 (sin (3pi)/5)` is ______.
The set of values of `sec^-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 value of the expression (cos–1x)2 is equal to sec2x.
The least numerical value, either positive or negative of angle θ is called principal value of the inverse trigonometric function.
The principal value of `sin^-1 [cos(sin^-1 1/2)]` is `pi/3`.
The period of the function f(x) = cos4x + tan3x is ____________.
The general solution of the equation `"cot" theta - "tan" theta = "sec" theta` is ____________ where `(n in I).`
If `"tan"^-1 "x" + "tan"^-1"y + tan"^-1 "z" = pi/2, "x,y,x" > 0,` then the value of xy+yz+zx is ____________.
Evaluate `sin^-1 (sin (3π)/4) + cos^-1 (cos π) + tan^-1 (1)`.
