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NDA 2025 Maths · Mathematics · Trigonometric Functions and Identities · medium

If sec θ+tan θ=2 with θ acute, then sin θ equals

Single correct option

If sec⁡θ+tan⁡θ=2\sec\theta+\tan\theta=2 with θ\theta acute, then sin⁡θ\sin\theta equals
  1. A. 45\dfrac45
  2. B. 53\dfrac53
  3. C. 34\dfrac34
  4. D. 35\dfrac35
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Answer: (D) 35\dfrac35

Since sec⁡2θ−tan⁡2θ=1\sec^2\theta-\tan^2\theta=1, we get sec⁡θ−tan⁡θ=12\sec\theta-\tan\theta=\frac12. Adding and subtracting: sec⁡θ=54\sec\theta=\frac54 and tan⁡θ=34\tan\theta=\frac34. Then sin⁡θ=tan⁡θcos⁡θ=34⋅45=35\sin\theta=\tan\theta\cos\theta=\frac34\cdot\frac45=\frac35.
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Original question written in the NDA 2025 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