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Home » \( r = \sqrt{\frac50\pi} \) - Dyverse

\( r = \sqrt{\frac50\pi} \) - Dyverse

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 Add the two expressions:

📌 f(x) = \sec^2 x + \cos^2 x + 2 + \csc^2 x + \sin^2 x - 2

📌 f(x) = \sec^2 x + \csc^2 x + (\cos^2 x + \sin^2 x) + 2 - 2 = \sec^2 x + \csc^2 x + 1

📌 Now express in terms of sine and cosine:

📌 f(x) = \frac{1}{\cos^2 x} + \frac{1}{\sin^2 x} + 1 = \frac{\sin^2 x + \cos^2 x}{\sin^2 x \cos^2 x} + 1 = \frac{1}{\sin^2 x \cos^2 x} + 1

📌 Using the identity $ \sin(2x) = 2\sin x \cos x $, we have:

📌 \sin x \cos x = \frac{1}{2} \sin 2x \Rightarrow \sin^2 x \cos^2 x = \frac{1}{4} \sin^2 2x

📌 f(x) = \frac{1}{\frac{1}{4} \sin^2 2x} + 1 = \frac{4}{\sin^2 2x} + 1

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\[ A = \sqrt{21 imes 8 imes 7 imes 6} \]
\[ A = \sqrt{21 imes 336} = \sqrt{7056} = 84 \]
Le rayon \( r \) du cercle inscrit est donnÃ© par :
\[ r = rac{A}{s} = rac{84}{21} = 4 \]
Le rayon du cercle inscrit est de 4.
La fonction \( f(x) = rac{x^2 - 1}{x - 1} \) n'est pas dÃ©finie pour...
Simplifions \( f(x) \) :
\[ f(x) = rac{(x-1)(x+1)}{x-1} \]
Pour \( x
eq 1 \), cela se simplifie en :

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