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

If tan θ=5/12, with θ acute, then sin 2θ equals

Single correct option

If tan⁡θ=512\tan\theta=\dfrac5{12}, with θ\theta acute, then sin⁡2θ\sin2\theta equals
  1. A. 120169\dfrac{120}{169}
  2. B. 513\dfrac{5}{13}
  3. C. 119169\dfrac{119}{169}
  4. D. 60169\dfrac{60}{169}
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Answer: (A) 120169\dfrac{120}{169}

Hypotenuse =13=13, so sin⁡θ=513\sin\theta=\frac5{13}, cos⁡θ=1213\cos\theta=\frac{12}{13} and sin⁡2θ=2⋅513⋅1213=120169\sin2\theta=2\cdot\frac{5}{13}\cdot\frac{12}{13}=\frac{120}{169}. Trap: 119169\frac{119}{169} is cos⁡2θ\cos2\theta.
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