Advertisements
Advertisements
प्रश्न
Find the principal value of `sin^-1 1/sqrt(2)`
उत्तर
Let y = `sin^-1 1/sqrt(2)`
Where `- pi/2 ≤ y ≤ pi/2`
sin y = `1/sqrt(2)`
= `sin (pi/4)`
y = `pi/4`
∴ The principal value of `sin^-1 1/sqrt(2) = pi/4`
APPEARS IN
संबंधित प्रश्न
Find the principal value of `cos^(-1) (sqrt3/2)`
Find the principal value of `tan^(-1) (-sqrt3)`
Find the value of the following:
`tan^(-1)(1) + cos^(-1) (-1/2) + sin^(-1) (-1/2)`
Prove that:
`tan^-1 ((sqrt(1 + x) - sqrt(1 - x))/(sqrt(1 + x) + sqrt(1 - x))) = pi/4 - 1/2 cos^-1 x`, for `- 1/sqrt2 <= x <= 1`
[Hint: put x = cos 2θ]
Find the domain of the following function:
`f(x)=sin^-1x+sin^-1 2x`
Solve for x:
`tan^-1 [(x-1),(x-2)] + tan^-1 [(x+1),(x+2)] = x/4`
In ΔABC, if a = 18, b = 24, c = 30 then find the values of sin `(A/2)`.
Find the principal value of the following: `sin^-1 (1/2)`
Find the principal value of the following: cosec- 1(2)
Find the principal value of the following: tan-1(– 1)
Prove the following:
`tan^-1["cosθ + sinθ"/"cosθ - sinθ"] = pi/(4) + θ, if θ ∈ (- pi/4, pi/4)`
Evaluate cot(tan−1(2x) + cot−1(2x))
Prove that `2 tan^-1 (3/4) = tan^-1(24/7)`
Prove that:
2 tan-1 (x) = `sin^-1 ((2x)/(1 + x^2))`
If 2sin2θ = 3cosθ, where 0 ≤ θ ≤ 2π, then θ = ______
If `tan^-1x + tan^-1y = (4pi)/5`, then `cot^-1x + cot^-1y` equals ______.
`(sin^-1(-1/2) + tan^-1(-1/sqrt(3)))/(sec^-1 (-2/sqrt(3)) + cos^-1(1/sqrt(2))` = ______.
If sin-1 x – cos-1 x `= pi/6,` then x = ____________.
`2tan^-1 (cos x) = tan^-1 (2"cosec" x)`, then 'x' will be equal to
Find the value of `cos(x/2)`, if tan x = `5/12` and x lies in third quadrant.
