Advertisements
Advertisements
प्रश्न
Find the principal value of the following:
`sec^-1(2tan (3pi)/4)`
Advertisements
उत्तर
Let `sec^-1(2tan (3pi)/4)=y`
Then,
`secy=2tan (3pi)/4`
We know that the range of the principal value branch is `[0,pi]-{pi/2}.`
Thus,
`secy = 2tan(3pi)/4=2xx(-1)=-2=sec((2pi)/3)`
`=>y=(2pi)/3in[0,pi]`
Hence, the principal value of `sec^-1(2tan (3pi)/4) is (2pi)/3.`
APPEARS IN
संबंधित प्रश्न
The principal solution of the equation cot x=`-sqrt 3 ` is
Find the value of `tan^(-1) sqrt3 - cot^(-1) (-sqrt3)`
Find the principal value of the following:
`sin^-1((sqrt3+1)/(2sqrt2))`
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)`
For the principal value, evaluate of the following:
`tan^-1{2sin(4cos^-1 sqrt3/2)}`
For the principal value, evaluate the following:
`tan^-1sqrt3-sec^-1(-2)`
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[cos{2\text(cosec)^-1(-2)}]`
Find the principal value of the following:
`cot^-1(-1/sqrt3)`
Find the principal value of the following:
`cot^-1(tan (3pi)/4)`
Solve for x, if:
tan (cos-1x) = `2/sqrt5`
If `sin^-1"x" + tan^-1"x" = pi/2`, prove that `2"x"^2 + 1 = sqrt5`
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 value of tan (cos–1x) and hence evaluate `tan(cos^-1 8/17)`
The principal value branch of sec–1 is ______.
The greatest and least values of (sin–1x)2 + (cos–1x)2 are respectively ______.
Let θ = sin–1 (sin (– 600°), then value of θ 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 ______.
The least numerical value, either positive or negative of angle θ is called principal value of the inverse trigonometric function.
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 "x" + "tan"^-1"y + tan"^-1 "z" = pi/2, "x,y,x" > 0,` then the value of xy+yz+zx is ____________.
What is the principal value of `cot^-1 ((-1)/sqrt(3))`?
What is the value of `tan^-1(1) cos^-1(- 1/2) + sin^-1(- 1/2)`
Evaluate `sin^-1 (sin (3π)/4) + cos^-1 (cos π) + tan^-1 (1)`.
