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NDA 2024 Maths · Mathematics · Properties of Triangles · easy

A triangle ABC is/are correct? 1. If no angle is a right angle, tan A+tan B+tan C=tan Atan Btan C. 2. The sum of any two sides is less than the third…

Single correct option

Which of the following statements about a triangle ABCABC is/are correct?
1. If no angle is a right angle, tan⁡A+tan⁡B+tan⁡C=tan⁡Atan⁡Btan⁡C\tan A+\tan B+\tan C=\tan A\tan B\tan C.
2. The sum of any two sides is less than the third side.
  1. A. 1 only
  2. B. 2 only
  3. C. Both 1 and 2
  4. D. Neither 1 nor 2
Show answer and solution

Answer: (A) 1 only

Since A+B=π−CA+B=\pi-C, tan⁡(A+B)=−tan⁡C\tan(A+B)=-\tan C gives tan⁡A+tan⁡B+tan⁡C=tan⁡Atan⁡Btan⁡C\tan A+\tan B+\tan C=\tan A\tan B\tan C; 1 is true. The triangle inequality says the sum of two sides is greater than the third, so 2 is false.
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Original question written in the NDA 2024 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