If A, B, C are acute positive angles such tha | vedclass

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Question

(a) $A + B + C = \pi $ 

$ \Rightarrow 	an A + 	an B + 	an C = 	an A	an B	an C$

Now $A.M.$ $\geq$ $G.M. $

$ \Rightarrow \frac{{	an

Vedclass · Accepted Answer

$K \le \frac{1}{{3\sqrt 3 }}$

Vedclass · Answer

(a) $A + B + C = \pi $ 

$ \Rightarrow 	an A + 	an B + 	an C = 	an A	an B	an C$

Now $A.M.$ $\geq$ $G.M. $

$ \Rightarrow \frac{{	an A + 	an B + 	an C}}{3} \ge {(	an A	an B	an C)^{1/3}}$

$ \Rightarrow \left( {\frac{{	an A	an B	an C}}{3}} ight) \ge {(	an A	an B	an C)^{1/3}}$ 

$ \Rightarrow {(	an A	an B	an C)^{2/3}} \ge 3$ 

$ \Rightarrow {\left( {\frac{1}{K}} ight)^{2/3}} \ge 3$

$\Rightarrow \frac{1}{K} \ge {3^{3/2}} $

$\Rightarrow K \le \frac{1}{{3\sqrt 3 }}$.

If $A, B, C$ are acute positive angles such that $A + B + C = \pi $ and $\cot A\,\cot \,B\,\cot \,C = K,$ then

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