Advertisements
Advertisements
Question
Find the principal value of the following:
`sec^-1(-sqrt2)`
Solution
Let `sec^-1(-sqrt2)=y`
Then,
`secy=-sqrt2`
We know that the range of the principal value branch is [0, π] - `{pi/2}`.
Thus,
`secy=-sqrt2=sec((3pi)/4)`
`=>y=(3pi)/4in[0,pi],y!=pi/2`
Hence, the principal value of `sec^-1(-sqrt2) is (3pi)/4.`
APPEARS IN
RELATED QUESTIONS
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)`
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 (3pi)/4)`
For the principal value, evaluate of the following:
`tan^-1{2sin(4cos^-1 sqrt3/2)}`
Find the principal value of the following:
`sec^-1(2sin (3pi)/4)`
For the principal value, evaluate the following:
`tan^-1sqrt3-sec^-1(-2)`
For the principal value, evaluate the following:
`sin^-1(-sqrt3/2)-2sec^-1(2tan pi/6)`
Find the principal value of the following:
`cosec^-1(-sqrt2)`
Find the principal value of the following:
cosec-1(-2)
Find the principal value of the following:
`\text(cosec)^-1(2/sqrt3)`
Find the principal value of the following:
`cosec^-1(2cos (2pi)/3)`
For the principal value, evaluate the following:
`cosec^-1(2tan (11pi)/6)`
Find the principal value of the following:
`cot^-1(tan (3pi)/4)`
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 principal value branch of sec–1 is ______.
The value of `sin^-1 (cos((43pi)/5))` is ______.
One branch of cos–1 other than the principal value branch corresponds to ______.
The domain of sin–1 2x is ______.
Let θ = sin–1 (sin (– 600°), then value of θ is ______.
The value of the expression sin [cot–1 (cos (tan–11))] is ______.
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 (- 1/sqrt(3)) + cot^-1(1/sqrt(3)) + tan^-1(sin((-pi)/2))`
Find the value of the expression `sin(2tan^-1 1/3) + cos(tan^-1 2sqrt(2))`
If `cos(sin^-1 2/5 + cos^-1x)` = 0, then x is equal to ______.
If tan–1x + tan–1y = `(4pi)/5`, then cot–1x + cot–1y equals ______.
The value of `cos^-1 (cos (14pi)/3)` 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 ____________.
`"cos" ["tan"^-1 {"sin" ("cot"^-1 "x")}]` is equal to ____________.
Which of the following is the principal value branch of `"cos"^-1 "x"`
