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

If tan A=2 and tan B=3, where A,B are acute angles, then A+B equals

Single correct option

If tan⁡A=2\tan A=2 and tan⁡B=3\tan B=3, where A,BA,B are acute angles, then A+BA+B equals
  1. A. 45∘45^\circ
  2. B. 135∘135^\circ
  3. C. 90∘90^\circ
  4. D. 120∘120^\circ
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Answer: (B) 135∘135^\circ

tan⁡(A+B)=2+31−6=−1\tan(A+B)=\dfrac{2+3}{1-6}=-1. Since tan⁡A>1\tan A>1 and tan⁡B>1\tan B>1, each angle exceeds 45∘45^\circ, so 90∘<A+B<180∘90^\circ<A+B<180^\circ. The only such angle with tangent −1-1 is 135∘135^\circ; 45∘45^\circ ignores the range.
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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