COMEDK · Maths · 1. Basic of Mathematics
If for real values of \(x, \cos \theta=x+\dfrac{1}{x}\), then
- A \(\theta\) is an obtuse angle.
- B No value of \(\theta\) is possible
- C \(\theta\) is an acute angle
- D \(\theta\) is right angle
Answer & Solution
Correct Answer
(B) No value of \(\theta\) is possible
Step-by-step Solution
Detailed explanation
Given the equation \(\cos \theta = x + \dfrac{1}{x}\) for real values of \(x\). For any real \(x \neq 0\), the expression \(x + \dfrac{1}{x}\) satisfies the inequality \(|x + \dfrac{1}{x}| \ge 2\) by the Arithmetic Mean-Geometric Mean inequality (AM-GM) for positive \(x\), and…
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