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NDA 2016 Maths · Mathematics · Trigonometric Functions and Identities · medium

If sec θ+tan θ=2 and θ is acute, then sin θ is equal to

Single correct option

If sec⁡θ+tan⁡θ=2\sec\theta+\tan\theta=2 and θ\theta is acute, then sin⁡θ\sin\theta is equal to
  1. A. 35\dfrac35
  2. B. 45\dfrac45
  3. C. 34\dfrac34
  4. D. 12\dfrac12
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Answer: (A) 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=\dfrac12. Adding and subtracting, sec⁡θ=54\sec\theta=\dfrac54 and tan⁡θ=34\tan\theta=\dfrac34. Hence cos⁡θ=45\cos\theta=\dfrac45 and sin⁡θ=tan⁡θcos⁡θ=35\sin\theta=\tan\theta\cos\theta=\dfrac35. The value 34\dfrac34 is tan⁡θ\tan\theta and 45\dfrac45 is cos⁡θ\cos\theta.
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Original question written in the NDA 2016 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