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NDA 2018 Maths · Mathematics · Trigonometric Functions and Identities · easy

Sin ^2θ+cos ^2θ=1 for every real θ. 2. sec θ can take a value between -1 and 1.

Single correct option

Consider the following statements: 1. sin⁡2θ+cos⁡2θ=1\sin^2\theta+\cos^2\theta=1 for every real θ\theta. 2. sec⁡θ\sec\theta can take a value between −1-1 and 11. Which of the statements given above 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: (A) 1 only

Statement 1 is the basic Pythagorean identity and holds for all real θ\theta. Since ∣cos⁡θ∣≤1|\cos\theta|\le1, ∣sec⁡θ∣≥1|\sec\theta|\ge1 wherever defined, so sec⁡θ\sec\theta never lies strictly between −1-1 and 11: statement 2 is false.
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Original question written in the NDA 2018 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