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NDA 2017 Maths · Mathematics · Straight Lines · medium

The tangent of the acute angle between the lines of slopes 2 and 3 is

Single correct option

The tangent of the acute angle between the lines of slopes 22 and 33 is
  1. A. 15\frac15
  2. B. 17\frac17
  3. C. 16\frac16
  4. D. 55
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Answer: (B) 17\frac17

tan⁡θ=∣m2−m11+m1m2∣=3−21+6=17\tan\theta=\left|\frac{m_2-m_1}{1+m_1m_2}\right|=\frac{3-2}{1+6}=\frac17. Writing 1−m1m2=−51-m_1m_2=-5 in the denominator gives 15\frac15 (the formula for the sum of angles), and 55 is tan⁡\tan of the sum of the inclinations' tangent product mix-up.
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Original question written in the NDA 2017 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