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NDA 1 2024 Maths, question 49

Topic: Trigonometry

Q49

What is the value of tan⁡65∘+2tan⁡45∘−2tan⁡40∘−tan⁡25∘\tan 65^{\circ}+2\tan 45^{\circ}-2\tan 40^{\circ}-\tan 25^{\circ} ?

  1. (a) 00
  2. (b) 11
  3. (c) 22Correct answer
  4. (d) 44

Solution.

Answer: (c) 22

  1. Use tan 65° = cot 25°.
  2. Then tan 65° − tan 25° = 2 cot 50° = 2 tan 40°.
  3. Substitution in the given expression leaves 2.