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NDA 1 2024 Maths, question 46

Topic: Trigonometry

Q46

In a triangle ABCABC, AB=16 cmAB=16\text{ cm}, BC=63 cmBC=63\text{ cm} and AC=65 cmAC=65\text{ cm}. What is the value of cos⁡2A+cos⁡2B+cos⁡2C\cos 2A+\cos 2B+\cos 2C ?

  1. (a) −1-1Correct answer
  2. (b) 00
  3. (c) 11
  4. (d) 7665\frac{76}{65}

Solution.

Answer: (a) −1-1

  1. Since 16² + 63² = 65², the angle opposite side 65 is a right angle.
  2. The remaining angles satisfy A + C = 90°, so cos 2A + cos 2C = 0.
  3. Adding cos 180° gives −1.