alleryStart learning →Assertion and reason: identities
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- Questions
- Reason
- It holds only where x lies in [−π/2, π/2], the principal branch.
- Verdict
- Both are true; the reason explains the assertion.
- Assertion
- sin⁻¹ (sin x) = x cannot be claimed for every real x.
- Reason
- [−1, 1] is exactly the domain of sin⁻¹.
- Verdict
- Both are true; the reason explains the assertion.
- Assertion
- sin (sin⁻¹ x) = x holds for every x in [−1, 1].
- Reason
- An inverse function swaps the roles of input and output.
- Verdict
- Both are true; the reason explains the assertion.
- Assertion
- If y = sin⁻¹ x then x = sin y.
Each pair turns on whether the stated interval is the right one. Source: syllabus Maths Part I, Ch 2 Inverse Trigonometric Functions.