Advertisements
Advertisements
प्रश्न
The value of cot (sin–1x) is ______.
विकल्प
`sqrt(1 + x^2)/x`
`x/sqrt(1 + x^2)`
`1/x`
`sqrt(1 - x^2)/x`
Advertisements
उत्तर
The value of cot (sin–1x) is `sqrt(1 - x^2)/x`.
Explanation:
Let sin–1x = θ, then sin θ = x
⇒ cosec θ = `1/x`
⇒ cosec2θ = `1/x^2`
⇒ 1 + cot2θ = `1/x^2`
⇒ cot θ = `sqrt(1 - x^2)/x`.
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(cos (3pi)/4)`
For the principal value, evaluate of the following:
`cos^-1 1/2 + 2 sin^-1 (1/2)`
Find the principal value of the following:
`tan^-1(-1/sqrt3)`
Find the principal value of the following:
`tan^-1(cos pi/2)`
Find the principal value of the following:
`tan^-1(2cos (2pi)/3)`
Find the principal value of the following:
`sec^-1(2)`
Find the principal value of the following:
`sec^-1(2sin (3pi)/4)`
For the principal value, evaluate the following:
`sin^-1[cos{2\text(cosec)^-1(-2)}]`
For the principal value, evaluate the following:
`cosec^-1(2tan (11pi)/6)`
Find the principal value of the following:
`cot^-1(-sqrt3)`
Find the principal value of the following:
`cot^-1(-1/sqrt3)`
Find the value of `tan^-1 (tan (9pi)/8)`.
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(2tan^-1 2/3) + cos(tan^-1 sqrt(3))`
Which of the following corresponds to the principal value branch of tan–1?
The value of `sin^-1 (cos((43pi)/5))` is ______.
One branch of cos–1 other than the principal value branch corresponds to ______.
The value of sin (2 sin–1 (.6)) is ______.
Find the value of `tan^-1 (tan (2pi)/3)`
Which of the following is the principal value branch of cosec–1x?
If `cos(sin^-1 2/5 + cos^-1x)` = 0, then x is equal to ______.
The value of the expression `2 sec^-1 2 + sin^-1 (1/2)` is ______.
If tan–1x + tan–1y = `(4pi)/5`, then cot–1x + cot–1y equals ______.
The principal value of `tan^-1 sqrt(3)` is ______.
The value of cos (sin–1x + cos–1x), |x| ≤ 1 is ______.
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 ____________.
The general solution of the equation `"cot" theta - "tan" theta = "sec" theta` is ____________ where `(n in I).`
If `"tan"^-1 ("a"/"x") + "tan"^-1 ("b"/"x") = pi/2,` then x is equal to ____________.
What is the principal value of `cot^-1 ((-1)/sqrt(3))`?
