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NDA 2 2024 Maths, question 31

Topic: Trigonometry

Q31

Consider the following numbers :

I. tan⁡22.5∘\tan 22.5^{\circ}

II. cot⁡22.5∘\cot 22.5^{\circ}

III. tan⁡22.5∘−cot⁡22.5∘\tan 22.5^{\circ}-\cot 22.5^{\circ}

How many of the above are irrational numbers?

  1. (a) None
  2. (b) Only one
  3. (c) Only twoCorrect answer
  4. (d) All three

Solution.

Answer: (c) Only two

  1. The half-angle value tan22.5°=√2−1 gives cot22.5°=√2+1.
  2. Both are irrational, but their difference is −2, which is rational.
  3. Exactly two of the listed numbers are irrational.