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NDA 2020 Maths · Mathematics · Trigonometric Functions and Identities · hard

If sec θ+tan θ=5, then sin θ equals

Single correct option

If sec⁡θ+tan⁡θ=5\sec\theta+\tan\theta=5, then sin⁡θ\sin\theta equals
  1. A. 513\dfrac{5}{13}
  2. B. 1213\dfrac{12}{13}
  3. C. 1312\dfrac{13}{12}
  4. D. 45\dfrac{4}{5}
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Answer: (B) 1213\dfrac{12}{13}

Since sec⁡2θ−tan⁡2θ=1\sec^2\theta-\tan^2\theta=1, we get sec⁡θ−tan⁡θ=15\sec\theta-\tan\theta=\frac15. Adding and subtracting gives sec⁡θ=135\sec\theta=\frac{13}5 and tan⁡θ=125\tan\theta=\frac{12}5. Then sin⁡θ=tan⁡θcos⁡θ=125⋅513=1213\sin\theta=\tan\theta\cos\theta=\frac{12}5\cdot\frac5{13}=\frac{12}{13}. The value 513\frac5{13} is cos⁡θ\cos\theta.
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Original question written in the NDA 2020 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