Advertisements
Advertisements
Question
Assertion (A): The domain of the function sec–12x is `(-∞, - 1/2] ∪ pi/2, ∞)`
Reason (R): sec–1(–2) = `- pi/4`
Options
Both A and R are true and R is the correct explanation of A.
Both A and R are true but R is not the correct explanation of A.
A is true but R is false.
A is false but R is true.
Solution
A is true but R is false.
Explanation:
sec–1x is defined if x ≤ −1 or x ≥ 1.
Hence, sec–12x will be defined if `x ≤ - 1/2` or `x ≥ 1/2`.
Hence, A is true.
The range of the function sec–1x is [0, π] − `{pi/2}`
R is false.
APPEARS IN
RELATED QUESTIONS
Find the value of the following:
`cos^(-1) (1/2) + 2 sin^(-1)(1/2)`
Find the domain of `f(x)=cotx+cot^-1x`
Find the principal value of the following: tan- 1( - √3)
Find the principal value of the following: cos- 1`(-1/2)`
Prove the following:
`tan^-1[sqrt((1 - cosθ)/(1 + cosθ))] = θ/(2)`, if θ ∈ (– π, π).
Find the principal solutions of the following equation:
sin 2θ = `− 1/(sqrt2)`
Evaluate cot(tan−1(2x) + cot−1(2x))
Prove that cot−1(7) + 2 cot−1(3) = `pi/4`
Find the principal value of the following:
`sin^-1 (- 1/2)`
Prove that `tan^-1 (m/n) - tan^-1 ((m - n)/(m + n)) = pi/4`
lf `sqrt3costheta + sintheta = sqrt2`, then the general value of θ is ______
If sin `(sin^-1 1/3 + cos^-1 x) = 1`, then the value of x is ______.
`tan[2tan^-1 (1/3) - pi/4]` = ______.
If 2sin2θ = 3cosθ, where 0 ≤ θ ≤ 2π, then θ = ______
If `tan^-1x + tan^-1y = (4pi)/5`, then `cot^-1x + cot^-1y` equals ______.
The value of `sin^-1[cos(pi/3)] + sin^-1[tan((5pi)/4)]` is ______.
Solve for x `tan^-1((1 - x)/(1 + x)) = 1/2 tan^-1x, x > 0`
The domain of the function y = sin–1 (– x2) is ______.
Show that `sin^-1 5/13 + cos^-1 3/5 = tan^-1 63/16`
`"sin" 265° - "cos" 265°` is ____________.
`"cos"^-1 ["cos" (2 "cot"^-1 (sqrt2 - 1))] =` ____________.
If A = `[(cosx, sinx),(-sinx, cosx)]`, then A1 A–1 is
The inverse of `f(x) = sqrt(3x^2 - 4x + 5)` is
Find the principal value of `tan^-1 (sqrt(3))`
`2tan^-1 (cos x) = tan^-1 (2"cosec" x)`, then 'x' will be equal to
what is the value of `cos^-1 (cos (13pi)/6)`
`cot^-1(sqrt(cos α)) - tan^-1 (sqrt(cos α))` = x, then sin x = ______.
If ax + b (sec (tan–1 x)) = c and ay + b (sec.(tan–1 y)) = c, then `(x + y)/(1 - xy)` = ______.
If tan 4θ = `tan(2/θ)`, then the general value of θ is ______.
Find the value of `tan^-1(x/y) + tan^-1((y - x)/(y + x))`
