eric lange
- 5829PVI PV
EricElric Eric"""" .
ericerikEricErikEricErikEricErk.
Ericvlog hustlerEricEric.
Eric Rohmer
Eric Clapton Eric Patrick ClaptonCBE1945330 Eric Clapt .
Eric Johnson
Eric (2024) 1979
Eric cash
300045908345.
Related Articles
Trending Articles
Shocking Duck Meme Shocked the Entire Internet—Don’t Miss What’s Going Viral!
Find the minimum value of \((\cos x + \sec x)^2 + (\sin x + \csc x)^2\).
To find the minimum value of the expression \((\cos x + \sec x)^2 + (\sin x + \csc x)^2\), let us start by rewriting \(\sec x\) and \(\csc x\) in terms of \(\cos x\) and \(\sin x\):
Let \(a = \cos x\) and \(b = \sin x\). Then:
This expands to:
a^2 + 2 + \frac{1}{a^2} + b^2 + 2 + \frac{1}{b^2}
Since \(a^2 + b^2 = \cos^2 x + \sin^2 x = 1\), the expression simplifies to:
+ 4 + \frac{1}{a^2} + \frac{1}{b^2} = 5 + \frac{1}{a^2} + \frac{1}{b^2}
We apply the AM-GM inequality to \(\frac{1}{a^2} + \frac{1}{b^2}\):
\frac{1}{a^2} + \frac{1}{b^2} \geq \frac{2}{ab}