AP EAMCET · Maths · Application of Derivatives
If \(A>0, B>0\) and \(A+B=\frac{\pi}{3}\), then the maximum value of \(\tan A \tan B\) is
- A \(\frac{1}{\sqrt 3}\)
- B \(\frac{1}{ 3}\)
- C \(\frac{1}{2}\)
- D \(\sqrt 3\)
Answer & Solution
Correct Answer
(B) \(\frac{1}{ 3}\)
Step-by-step Solution
Detailed explanation
Given, \(A+B=\frac{\pi}{3}\) Let \(y=\tan A \tan B\) \(y=\tan A \tan \left(\frac{\pi}{3}-A\right)\) Differentiating w.r.t A, we get \(\Rightarrow \frac{d y}{d A}=\sec ^2 A \tan \left(\frac{\pi}{3}-A\right)-\sec ^2\left(\frac{\pi}{3}-A\right) \tan A\) For maxima or minima,…
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