Question
Consider the following for the two (02) items that follow: Let p = | - ( - 90°)|. What is the minimum value of p?
NDA
Mathematics
Trigonometric Ratios & Identities
2025
NDA 2025 (Phase 1)
NDA Mathematics Question (2025) — Solution
Options
- A. 0
- B. 1 2
- C. 1 2
- D. 1
Answer
A. 0
Step-by-step solution
p = | - ( - 90^ )| Using the trigonometric identity ( - 90^ ) = - (90^ - ) = - , we get: p = | - (- )| = | + | Multiplying and dividing the expression inside the modulus by 2 : p = 2 | 1 2 + 1 2 | p = 2 | ( + 45^ )| Since the absolute value of any real expression is non-negative, the minimum possible value of p is 0. This minimum is achieved when ( + 45^ ) = 0, which occurs at = -45^ . Therefore, the minimum value of p is 0.
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