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NDA 2 2025 Maths, question 27

Topic: Trigonometry

Passage · Q27 to Q28

Let p=cosec⁡20∘p=\operatorname{cosec} 20^{\circ} and q=cosec⁡70∘q=\operatorname{cosec} 70^{\circ}.

Q27

What is (3p4−q4)\left( \frac{\sqrt{3}p}{4}-\frac{q}{4} \right) equal to?

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

Solution.

Answer: (c) 11

  1. Since sin70°=cos20°, the expression is (√3 cos20°−sin20°)/(4 sin20° cos20°).
  2. The numerator is 2 cos50°=2 sin40°, and the denominator is 2 sin40°.
  3. Their ratio is 1.