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NDA 2024 Maths · Mathematics · Trigonometric Functions and Identities · hard

Sin ^2θ+cos ^2θ=1 for all real θ. 2. sec ^2θ-tan ^2θ=1 for all real θ.

Single correct option

Which of the statements is/are correct?
1. sin⁡2θ+cos⁡2θ=1\sin^2\theta+\cos^2\theta=1 for all real θ\theta.
2. sec⁡2θ−tan⁡2θ=1\sec^2\theta-\tan^2\theta=1 for all real θ\theta.
  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 an identity valid for every real θ\theta. Statement 2 holds only where cos⁡θ≠0\cos\theta\ne0; at θ=π/2\theta=\pi/2 both sec⁡\sec and tan⁡\tan are undefined, so 'for all real θ\theta' is false.
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Original question written in the NDA 2024 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