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NDA 2018 Maths · Mathematics · Trigonometric Functions and Identities · medium

If sin θ+cos θ=7/5, what is the value of sin θcos θ?

Single correct option

If sin⁡θ+cos⁡θ=75\sin\theta+\cos\theta=\dfrac75, what is the value of sin⁡θcos⁡θ\sin\theta\cos\theta?
  1. A. 2425\dfrac{24}{25}
  2. B. 15\dfrac{1}{5}
  3. C. 1225\dfrac{12}{25}
  4. D. 4925\dfrac{49}{25}
Show answer and solution

Answer: (C) 1225\dfrac{12}{25}

Square both sides: 1+2sin⁡θcos⁡θ=49251+2\sin\theta\cos\theta=\dfrac{49}{25}, so 2sin⁡θcos⁡θ=24252\sin\theta\cos\theta=\dfrac{24}{25} and sin⁡θcos⁡θ=1225\sin\theta\cos\theta=\dfrac{12}{25}. The distractor 24/2524/25 is the value of sin⁡2θ\sin2\theta.
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Original question written in the NDA 2018 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