Advertisements
Advertisements
Question
Find the value, if it exists. If not, give the reason for non-existence
`sin^-1 [sin 5]`
Advertisements
Solution
`- pi/2 ≤ sin^-1 5 ≤ pi/2`
`- 3 pi/2 ≤ 5 ≤ 2pi`
`- pi/2 ≤ 5 - 2pi ≤ 0 ≤ pi/2`
sin(5 – 2π) = sin 5
sin–1(sin 5) = 5 – 2π
APPEARS IN
RELATED QUESTIONS
Solve for x : tan-1 (x - 1) + tan-1x + tan-1 (x + 1) = tan-1 3x
Prove the following:
3cos−1x = cos−1(4x3 − 3x), `x ∈ [1/2, 1]`
Write the following function in the simplest form:
`tan^(-1) (sqrt(1+x^2) -1)/x`, x ≠ 0
Write the function in the simplest form: `tan^(-1) ((cos x - sin x)/(cos x + sin x)) `,` 0 < x < pi`
Find the value of the given expression.
`tan(sin^(-1) 3/5 + cot^(-1) 3/2)`
Find the value, if it exists. If not, give the reason for non-existence
`sin^-1 (cos pi)`
Find the number of solutions of the equation `tan^-1 (x - 1) + tan^-1x + tan^-1(x + 1) = tan^-1(3x)`
Choose the correct alternative:
`sin^-1 (tan pi/4) - sin^-1 (sqrt(3/x)) = pi/6`. Then x is a root of the equation
Choose the correct alternative:
sin(tan–1x), |x| < 1 is equal to
Show that `tan(1/2 sin^-1 3/4) = (4 - sqrt(7))/3` and justify why the other value `(4 + sqrt(7))/3` is ignored?
The value of cot–1(–x) for all x ∈ R in terms of cot–1x is ______.
If tan-1 2x + tan-1 3x = `pi/4,` then x is ____________.
If x = a sec θ, y = b tan θ, then `("d"^2"y")/("dx"^2)` at θ = `π/6` is:
`"sin"^-1 (1/sqrt2)`
The Simplest form of `cot^-1 (1/sqrt(x^2 - 1))`, |x| > 1 is
What is the simplest form of `tan^-1 sqrt(1 - x^2 - 1)/x, x ≠ 0`
The set of all values of k for which (tan–1 x)3 + (cot–1 x)3 = kπ3, x ∈ R, is the internal ______.
If `cos^-1(2/(3x)) + cos^-1(3/(4x)) = π/2(x > 3/4)`, then x is equal to ______.
If `tan^-1 ((x - 1)/(x + 1)) + tan^-1 ((2x - 1)/(2x + 1)) = tan^-1 (23/36)` = then prove that 24x2 – 23x – 12 = 0
The value of cosec `[sin^-1((-1)/2)] - sec[cos^-1((-1)/2)]` is equal to ______.
