The principal value of sin⁻¹(x) lies in the interval:
A
[-π/2, π/2]
B
[0, π]
C
[0, 2π]
D
[-π, π]
Analysis & Theory
The principal value of sin⁻¹(x) is defined in [-π/2, π/2].
The principal value of cos⁻¹(x) lies in the interval:
A
[0, π]
B
[-π/2, π/2]
C
[-π, π]
D
[0, 2π]
Analysis & Theory
The principal value of cos⁻¹(x) is defined in [0, π].
The principal value of tan⁻¹(x) lies in the interval:
A
(-π/2, π/2)
B
[0, π]
C
[0, 2π]
D
[-π, π]
Analysis & Theory
The principal value of tan⁻¹(x) is defined in (-π/2, π/2).
sin(sin⁻¹ x) equals:
A
x
B
1/x
C
√(1-x²)
D
cos x
Analysis & Theory
For x in [-1,1], sin(sin⁻¹ x) = x.
cos(cos⁻¹ x) equals:
A
x
B
1/x
C
√(1-x²)
D
sin x
Analysis & Theory
For x in [-1,1], cos(cos⁻¹ x) = x.
tan(tan⁻¹ x) equals:
A
x
B
1/x
C
√(1+x²)
D
cot x
Analysis & Theory
For x ∈ R, tan(tan⁻¹ x) = x.
sin⁻¹(sin x) equals:
A
x if x ∈ [-π/2, π/2]
B
x if x ∈ [0, π]
C
x for all x
D
π - x
Analysis & Theory
sin⁻¹(sin x) = x only if x lies in the principal interval [-π/2, π/2].
cos⁻¹(cos x) equals:
A
x if x ∈ [0, π]
B
x if x ∈ [-π/2, π/2]
C
x for all x
D
π - x
Analysis & Theory
cos⁻¹(cos x) = x only if x lies in the principal interval [0, π].
tan⁻¹(tan x) equals:
A
x if x ∈ (-π/2, π/2)
B
x if x ∈ [0, π]
C
x for all x
D
π - x
Analysis & Theory
tan⁻¹(tan x) = x only if x lies in the principal interval (-π/2, π/2).
The relation between sin⁻¹ x and cos⁻¹ x is:
A
sin⁻¹ x + cos⁻¹ x = π/2
B
sin⁻¹ x - cos⁻¹ x = π/2
C
sin⁻¹ x * cos⁻¹ x = 1
D
sin⁻¹ x / cos⁻¹ x = 1
Analysis & Theory
For x ∈ [-1,1], sin⁻¹ x + cos⁻¹ x = π/2.
The relation between tan⁻¹ x and cot⁻¹ x is:
A
tan⁻¹ x + cot⁻¹ x = π/2
B
tan⁻¹ x - cot⁻¹ x = π/2
C
tan⁻¹ x * cot⁻¹ x = 1
D
tan⁻¹ x / cot⁻¹ x = 1
Analysis & Theory
For x ∈ R, tan⁻¹ x + cot⁻¹ x = π/2.