Trigonometrical Ratios and Identities 3 Question 2
3. If $A>0, B>0$ and $A+B=\pi / 3$, then the maximum value of $\tan A \tan B$ is
(1993)
Analytical & Descriptive Question
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Answer:
Correct Answer: 3. $\frac{1}{3}$
Solution:
- Since, $A+B=\frac{\pi}{3}$ and, we know product of term is maximum, when values are equal.
$\therefore(\tan A \cdot \tan B)$ is maximum.
When $A=B=\pi / 6$
i.e.
$$ y=\tan \frac{\pi}{6} \tan \frac{\pi}{6}=\frac{1}{3} $$
