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NDA 1 2024 Maths, question 50

Topic: Trigonometry

Q50

Consider the following statements :

  1. In a triangle ABCABC, if cot⁡A⋅cot⁡B⋅cot⁡C>0\cot A\cdot \cot B\cdot \cot C>0, then the triangle is an acute angled triangle.

  2. In a triangle ABCABC, if tan⁡A⋅tan⁡B⋅tan⁡C>0\tan A\cdot \tan B\cdot \tan C>0, then the triangle is an obtuse angled triangle.

Which of the statements given above is/are correct ?

  1. (a) 1 onlyCorrect answer
  2. (b) 2 only
  3. (c) Both 1 and 2
  4. (d) Neither 1 nor 2

Solution.

Answer: (a) 1 only

  1. In an obtuse triangle exactly one cotangent is negative, while the other two are positive; their product is negative.
  2. A positive product therefore requires an acute triangle.
  3. The proposed further restriction in statement 2 does not follow.
  4. Only statement 1 is correct.