Two are true, one is not

Exercise and reference answers

Questions

1. False statement

   tan⁻¹ has domain [−1, 1]

   Statements

   1. tan⁻¹ has domain [−1, 1]
   2. sin⁻¹ has domain [−1, 1]
   3. cos⁻¹ has principal range [0, π]

2. False statement

   sec⁻¹ removes 0 from its range

   Statements

   1. cot⁻¹ has principal range (0, π)
   2. sec⁻¹ removes 0 from its range
   3. cosec⁻¹ has domain R − (−1, 1)

3. False statement

   Every trigonometric function is one-one on its natural domain

   Statements

   1. The principal value of an inverse lies in its principal branch
   2. sin (sin⁻¹ x) = x for x in [−1, 1]
   3. Every trigonometric function is one-one on its natural domain

Explanation