Question

Find the value of cos-1 (cos x), x∈ [0, π]
1. x
2. -x
3. π + x
4. π - x

Answer 1

Correct Answer - Option 1 : x

Concept used:

Principal Values of Inverse Trigonometric Functions:

Function	Domain	Range of Principal Value
sin-1 x	[-1, 1]	[-π/2, π/2]
cos-1 x	[-1, 1]	[0, π]
csc-1 x	R - (-1, 1)	[-π/2, π/2] - {0}
sec-1 x	R - (-1, 1)	[0, π] - {π/2}
tan-1 x	R	(-π/2, π/2)
cot-1 x	R	(0, π)

Calculation:

Given: x ∈ [0, π] 

cos-1 (cos x) = x