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Home » h^2 + 5^2 = 13^2 - Abu Waleed Tea

h^2 + 5^2 = 13^2 - Abu Waleed Tea

📅 February 28, 2026 👤 scraface

Feb 28, 2026

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📌 To solve \(\tan 45^\circ + \tan 30^\circ\), we first find the values of \(\tan 45^\circ\) and \(\tan 30^\circ\).

📌 \tan 45^\circ = 1

📌 For \(\tan 30^\circ\), we use the identity for the tangent of 30 degrees:

📌 \tan 30^\circ = \frac{1}{\sqrt{3}}

📌 Adding these values together, we have:

📌 \tan 45^\circ + \tan 30^\circ = 1 + \frac{1}{\sqrt{3}}

📌 To express this in a single fraction, find a common denominator:

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a + b + c \geq 3\sqrt[3]{abc} = 3.
Equality occurs when $ a = b = c = 1 $, i.e., when $ x = y = z $.
Now consider the second term:
\log\left(b + rac{1}{b}
ight) \geq \log(2),
with equality when $ b = 1 $, i.e., $ y = z $.
Thus, the minimum value of the entire expression is
- \log(2).
This value is achievable when $ x = y = z $, so the minimum is
oxed{3 - \log 2}.

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