11The given expression = \frac{2}{a}-a, where 0\le a\le 1 so \frac{2}{a}-a\ge 2-(1-\Delta )\ge 1......where \Delta \ge 0, thus equality at 1, with \Delta = 0...........
If 0 <x < π/2, then the Minimum Value of....
\frac{cos^{3}x}{sin \ x} + \frac{sin^{3}x}{cos \ x} is ...
a) √3 b) 1/2 c) 1/3 d) 1
-
UP 0 DOWN 0 0 6
6 Answers
111try using
\frac{cos^3x}{sinx}=\frac{cos3x+3cosx}{4sinx} and
\frac{sin^3x}{cosx}=\frac{3sinx-sin3x}{4cosx}
341By Cauchy Schwarz (Titu's lemma),
\frac{\cos^4 x}{\sin x \cos x} + \frac{\sin^4 x}{\sin x \cos x} \ge \frac{(\sin^2 x + \cos^2 x)^2}{2 \sin x \cos x} = \frac{1}{\sin 2x} \ge 1
13Thanku Prophet sir.....
@Soumik - Bhai plz explain ; kuch samajh nahi aaya...
1theprophet sir nice solution
avik you can learn titu's lemma here http://www.artofproblemsolving.com/Forum/weblog_entry.php?t=264227