Assertion and reason: identities

Exercise and reference answers

Questions

1. 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.

2. 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].

3. 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.

Explanation