Question
For the following two (02) items: Let p = cosec \, 20° and q = cosec \, 70°. What is p^2 + q^2 p^2 q^2 equal to?
NDA
Mathematics
Trigonometric Ratios & Identities
2025
NDA 2025 (Phase 2)
NDA Mathematics Question (2025) — Solution
Options
- A. 1 2
- B. 1
- C. 3 2
- D. 2
Answer
B. 1
Step-by-step solution
Given p = cosec \, 20^ and q = cosec \, 70^ . The given expression is p^2 + q^2 p^2 q^2 . This can be rewritten as 1 q^2 + 1 p^2 . Substituting the values of p and q: 1 cosec ^2 70^ + 1 cosec ^2 20^ = ^2 70^ + ^2 20^ Since 70^ = (90^ - 20^ ) = 20^ , we get: = ^2 20^ + ^2 20^ = 1 Answer: 1
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