Assertion and reason

Exercise and reference answers

Questions

1. Reason

   The sine function never takes a value outside [−1, 1].

   Verdict

   Both are true; the reason explains the assertion.

   Assertion

   sin⁻¹ is defined only on [−1, 1].

2. Reason

   The tangent function takes every real value on (−π/2, π/2).

   Verdict

   Both are true; the reason explains the assertion.

   Assertion

   tan⁻¹ is defined for every real number.

3. Reason

   cosec x is undefined at integral multiples of π, and 0 is one of them.

   Verdict

   Both are true; the reason explains the assertion.

   Assertion

   The principal range of cosec⁻¹ has 0 removed.

4. Reason

   The superscript −1 always denotes a reciprocal.

   Verdict

   The assertion is false and the reason is true.

   Assertion

   sin⁻¹ x is the same as 1/sin x.

Explanation