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NDA 1 2024 Maths, question 36

Topic: Trigonometry

Q36

What is 3cos⁡10∘−sin⁡10∘sin⁡25∘cos⁡25∘\frac{\sqrt{3}\cos 10^{\circ}-\sin 10^{\circ}}{\sin 25^{\circ}\cos 25^{\circ}} equal to ?

  1. (a) 11
  2. (b) 3\sqrt{3}
  3. (c) 22
  4. (d) 44Correct answer

Solution.

Answer: (d) 44

  1. Use √3 cos 10° − sin 10° = 2 cos 40° = 2 sin 50°.
  2. Also sin 25° cos 25° = ½ sin 50°.
  3. Their ratio is 4.