Write the difference between maximum and minimum values of sin–1x fo

1.	Write the difference between maximum and minimum values of sin–1x for x ∈ [–1, 1].
Answer» Let f (x) = sin^-1 x For x to be defined, -1 ≤ x ≤ 1 For -1 ≤ x ≤ 1, sin^-1(-1) ≤ sin^-1 x ≤ sin^-1(1) ⇒ -π/2 ≤ sin^-1 x ≤ π/2 ⇒ -π/2 ≤ f (x) ≤ π/2 Maximum value = π/2 and minimum value = -π/2 ∴ The difference between maximum and minimum values of sin^-1 x = π/2 – (-π/2) = 2π/2 = π

Write the difference between maximum and minimum values of sin–1x for x ∈ [–1, 1].

Answer»

Let f (x) = sin^-1 x

For x to be defined, -1 ≤ x ≤ 1

For -1 ≤ x ≤ 1, sin^-1(-1) ≤ sin^-1 x ≤ sin^-1(1)

⇒ -π/2 ≤ sin^-1 x ≤ π/2

⇒ -π/2 ≤ f (x) ≤ π/2

Maximum value = π/2 and minimum value = -π/2

∴ The difference between maximum and minimum values of

sin^-1 x = π/2 – (-π/2) = 2π/2 = π