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

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

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

Similar Questions

$2 \sin \left(\frac{\pi}{22}\right) \sin \left(\frac{3 \pi}{22}\right) \sin \left(\frac{5 \pi}{22}\right) \sin \left(\frac{7 \pi}{22}\right) \sin \left(\frac{9 \pi}{22}\right)$ is

${\sin ^2}\frac{\pi }{8} + {\sin ^2}\frac{{3\pi }}{8} + {\sin ^2}\frac{{5\pi }}{8} + {\sin ^2}\frac{{7\pi }}{8} = $

$\frac{{\cos 12^\circ - \sin 12^\circ }}{{\cos 12^\circ + \sin 12^\circ }} + \frac{{\sin 147^\circ }}{{\cos 147^\circ }} = $

If $\frac{{5\pi }}{2} < x < 3\pi $, then the value of the expression $\frac{{\sqrt {1 - \sin x} + \sqrt {1 + \sin x} }}{{\sqrt {1 - \sin x} - \sqrt {1 + \sin x} }}$ is

The value of $\sum_{r-1}^{18} cos^2(5r)^o,$ where $x^o $ denotes the $x$ degree, is equals to