PrepRung
Sign inSign up free

NDA 2017 Maths · Mathematics · Trigonometric Functions and Identities · easy

Tan x is defined for all real x. 2. The range of sin x is the open interval (-1,1).

Single correct option

Consider the following statements.

1. tan⁡x\tan x is defined for all real xx.
2. The range of sin⁡x\sin x is the open interval (−1,1)(-1,1).

Which of the statements is/are correct?
  1. A. 1 only
  2. B. 2 only
  3. C. Both 1 and 2
  4. D. Neither 1 nor 2
Show answer and solution

Answer: (D) Neither 1 nor 2

tan⁡x=sin⁡xcos⁡x\tan x=\frac{\sin x}{\cos x} is undefined where cos⁡x=0\cos x=0, e.g. x=π2x=\frac\pi2, so statement 1 is false. sin⁡x\sin x attains ±1\pm1, so its range is the closed interval [−1,1][-1,1] and statement 2 is false. Neither is correct.
Report a mistake

Original question written in the NDA 2017 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake