Advertisements
Advertisements
प्रश्न
Find the principal value of `cos^(-1) (sqrt3/2)`
उत्तर
Let `cos^(-1) (sqrt3/2) = y," Then " cos y = sqrt3/2 = cos (pi/6)`
We know that the range of the principal value branch of cos−1 is
`[0, pi] and cos (pi/6) = sqrt3/2`
Therefore, the priciple value of `cos^(-1) (sqrt3/2) is pi/6`
APPEARS IN
संबंधित प्रश्न
`tan^(-1) sqrt3 - sec^(-1)(-2)` is equal to ______.
Find the principal value of `sin^-1(1/sqrt2)`
Find the domain of the following function:
`f(x) = sin^-1x + sinx`
Evaluate the following:
`tan^-1(-1/sqrt3)+tan^-1(-sqrt3)+tan^-1(sin(-pi/2))`
Find the domain of `f(x)=cotx+cot^-1x`
Evaluate the following:
`cot^-1 1/sqrt3-\text(cosec)^-1(-2)+sec^-1(2/sqrt3)`
In ΔABC, if a = 18, b = 24, c = 30 then find the values of cos `A/2`
In ΔABC, if a = 18, b = 24, c = 30 then find the values of sinA
Find the principal value of the following: tan-1(– 1)
Find the principal value of the following: cos- 1`(-1/2)`
Evaluate the following:
`"cosec"^-1(-sqrt(2)) + cot^-1(sqrt(3))`
Prove the following:
`2tan^-1(1/3) = tan^-1(3/4)`
If tan−1x + tan−1y + tan−1z = π, then show that `1/(xy) + 1/(yz) + 1/(zx)` = 1
Prove that `2 tan^-1 (1/8) + tan^-1 (1/7) + 2tan^-1 (1/5) = pi/4`
Find the principal value of the following:
`sin^-1 (- 1/2)`
Find the principal value of the following:
cosec-1 (2)
Prove that:
2 tan-1 (x) = `sin^-1 ((2x)/(1 + x^2))`
Evaluate: `cos (sin^-1 (4/5) + sin^-1 (12/13))`
In Δ ABC, with the usual notations, if sin B sin C = `"bc"/"a"^2`, then the triangle is ______.
sin[3 sin-1 (0.4)] = ______.
If `sin^-1 3/5 + cos^-1 12/13 = sin^-1 P`, then P is equal to ______
The value of cot (- 1110°) is equal to ______.
If 2sin2θ = 3cosθ, where 0 ≤ θ ≤ 2π, then θ = ______
If 2 tan–1(cos θ) = tan–1(2 cosec θ), then show that θ = π 4, where n is any integer.
`"sin" ["cot"^-1 {"cos" ("tan"^-1 "x")}] =` ____________.
`"cos"^-1 ["cos" (2 "cot"^-1 (sqrt2 - 1))] =` ____________.
3 tan-1 a is equal to ____________.
Which of the following functions is inverse of itself?
Values of tan–1 – sec–1(–2) is equal to
Assertion (A): The domain of the function sec–12x is `(-∞, - 1/2] ∪ pi/2, ∞)`
Reason (R): sec–1(–2) = `- pi/4`
Let x = sin–1(sin8) + cos–1(cos11) + tan–1(tan7), and x = k(π – 2.4) for an integer k, then the value of k is ______.
If sin–1a + sin–1b + sin–1c = π, then find the value of `asqrt(1 - a^2) + bsqrt(1 - b^2) + csqrt(1 - c^2)`.
If x ∈ R – {0}, then `tan^-1 ((sqrt(1 + x^2) + sqrt(1 - x^2))/(sqrt(1 + x^2) - sqrt(1 - x^2)))`
Find the value of `cos(x/2)`, if tan x = `5/12` and x lies in third quadrant.
Prove that:
tan–1x + tan–1y = `π + tan^-1((x + y)/(1 - xy))`, provided x > 0, y > 0, xy > 1
Solve for x:
5tan–1x + 3cot–1x = 2π