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NDA 2 2025 Maths, question 28

Topic: Trigonometry

Passage · Q27 to Q28

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

Q28

What is p2+q2p2q2\frac{p^{2}+q^{2}}{p^{2}q^{2}} equal to?

  1. (a) 12\frac{1}{2}
  2. (b) 11Correct answer
  3. (c) 32\frac{3}{2}
  4. (d) 22

Solution.

Answer: (b) 11

  1. Split the fraction.
  2. (p²+q²)/(p²q²)=1/q²+1/p²=sin²70°+sin²20°=cos²20°+sin²20°=1.