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NDA 2 2024 Maths, question 25

Topic: Trigonometry

Q25

In a triangle ABCABC, ∠A=75∘\angle A=75^{\circ} and ∠B=45∘\angle B=45^{\circ}. What is 2a−b2a-b equal to?

  1. (a) cc
  2. (b) 2c\sqrt{2}cCorrect answer
  3. (c) 2c2c
  4. (d) 22c2\sqrt{2}c

Solution.

Answer: (b) 2c\sqrt{2}c

  1. C=180°−75°−45°=60°.
  2. By the sine rule, (2a−b)/c=(2sin75°−sin45°)/sin60°.
  3. Using sin75°=(√6+√2)/4, the numerator is √6/2.
  4. Division by √3/2 gives √2, so 2a−b=√2c.