Advertisements
Advertisements
प्रश्न
Find the principal value of cos–1x, for x = `sqrt(3)/2`.
उत्तर
If `cos^-1 (sqrt(3)/2)` = θ, then cos θ = `sqrt(3)/2`
Since we are considering principal branch, θ ∈ [0, π].
Also, since `sqrt(3)/2` > 0, θ being in he first quadrant
Hence `cos^-1 (sqrt(3)/2) = pi/6`
APPEARS IN
संबंधित प्रश्न
Write the principal value of `tan^(-1)+cos^(-1)(-1/2)`
Find the principal value of the following:
`sin^-1(cos (3pi)/4)`
Find the principal value of the following:
`tan^-1(-1/sqrt3)`
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(2tan (3pi)/4)`
Find the principal value of the following:
`\text(cosec)^-1(2/sqrt3)`
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)`
if sec-1 x = cosec-1 v. show that `1/x^2 + 1/y^2 = 1`
Find the value of `sin[2cot^-1 ((-5)/12)]`
Find the values of x which satisfy the equation sin–1x + sin–1(1 – x) = cos–1x.
The domain of sin–1 2x is ______.
The greatest and least values of (sin–1x)2 + (cos–1x)2 are respectively ______.
The value of `tan(cos^-1 3/5 + tan^-1 1/4)` is ______.
Find the value of `tan^-1 (- 1/sqrt(3)) + cot^-1(1/sqrt(3)) + tan^-1(sin((-pi)/2))`
The value of sin (2 tan–1(0.75)) is equal to ______.
The value of `cos^-1 (cos (3pi)/2)` is equal to ______.
The value of the expression `2 sec^-1 2 + sin^-1 (1/2)` is ______.
The value of `cot[cos^-1 (7/25)]` is ______.
The result `tan^1x - tan^-1y = tan^-1 ((x - y)/(1 + xy))` is true when value of xy is ______.
The least numerical value, either positive or negative of angle θ is called principal value of the inverse trigonometric function.
The period of the function f(x) = cos4x + tan3x is ____________.
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 ____________.
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 value of x so that the seven-digit number 8439 × 53 is divisible by 99?
Evaluate `sin^-1 (sin (3π)/4) + cos^-1 (cos π) + tan^-1 (1)`.
