JEE Mains · Maths · STD 11 - 8. sequence and series
Let the range of the function \(f(x)=\frac{1}{2+\sin 3 x+\cos 3 x}, x \in \operatorname{IR} \text { be }[a, b] .\) If \(\alpha\) and \(\beta\) are respectively the \(A.M.\) and the \(G.M.\) of a and \(b\), then \(\frac{\alpha}{\beta}\) is equal to :
- A \(\sqrt{2}\)
- B \(2\)
- C \(\sqrt{\pi}\)
- D \(\pi\)
Answer & Solution
Correct Answer
(A) \(\sqrt{2}\)
Step-by-step Solution
Detailed explanation
\( f(x) \frac{1}{2+\sin 3 x+\cos 3 x} \) \( {\left[\frac{1}{2+\sqrt{2}}, \frac{1}{2-\sqrt{2}}\right]} \) \( \frac{\alpha}{\beta}=\frac{a+b}{2 \sqrt{a b}}=\frac{1}{2}\left(\sqrt{\frac{a}{b}}+\sqrt{\frac{b}{a}}\right) \)…
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