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Which of these statements never can be true? A) tanx = 500 B) Cosx =0,999 () sinxcosx 5,000 = Q) Sinx = cosx

Which of these statements never can be true? A) tanx = 500 B) Cosx =0,999 () sinxcosx 5,000 = Q) Sinx = cosx

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
### Trigonometric Problem: Which Statement Can Never Be True? Consider the following trigonometric statements and determine which one can never be true: A) \(\tan(x) = 500\) B) \(\cos(x) = 0.999\) C) \(\sin(x) + \cos(x) = 5.000\) D) \(\sin(x) = \cos(x)\) #### Explanation: - **Option A:** \(\tan(x) = 500\) is possible since the tangent function can take any real value. - **Option B:** \(\cos(x) = 0.999\) is possible because the cosine function ranges from -1 to 1. - **Option C:** \(\sin(x) + \cos(x) = 5.000\) is impossible because the maximum value of \(\sin(x) + \cos(x)\) is \(\sqrt{2}\) when \(\sin(x) = \cos(x)\). - **Option D:** \(\sin(x) = \cos(x)\) is possible when \(x = \frac{\pi}{4} + n\pi\), where \(n\) is an integer. Thus, the statement that can never be true is **C**: \(\sin(x) + \cos(x) = 5.000\).
Transcribed Image Text:### Trigonometric Problem: Which Statement Can Never Be True? Consider the following trigonometric statements and determine which one can never be true: A) \(\tan(x) = 500\) B) \(\cos(x) = 0.999\) C) \(\sin(x) + \cos(x) = 5.000\) D) \(\sin(x) = \cos(x)\) #### Explanation: - **Option A:** \(\tan(x) = 500\) is possible since the tangent function can take any real value. - **Option B:** \(\cos(x) = 0.999\) is possible because the cosine function ranges from -1 to 1. - **Option C:** \(\sin(x) + \cos(x) = 5.000\) is impossible because the maximum value of \(\sin(x) + \cos(x)\) is \(\sqrt{2}\) when \(\sin(x) = \cos(x)\). - **Option D:** \(\sin(x) = \cos(x)\) is possible when \(x = \frac{\pi}{4} + n\pi\), where \(n\) is an integer. Thus, the statement that can never be true is **C**: \(\sin(x) + \cos(x) = 5.000\).
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