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Home » \frac1\sin x \cos x = 2\sqrt2. - DNSFLEX

\frac1\sin x \cos x = 2\sqrt2. - DNSFLEX

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 Let the legs of the right triangle be $ 3k $ and $ 4k $, so the hypotenuse is $ h = 5k $ by the Pythagorean theorem.

📌 The inradius $ r $ of a right triangle is given by the formula:

📌 r = \frac{a + b - c}{2}

📌 where $ a $ and $ b $ are the legs and $ c $ is the hypotenuse. Substituting:

📌 r = \frac{3k + 4k - 5k}{2} = \frac{2k}{2} = k

📌 So $ k = r $. Now compute the area of the triangle:

📌 \text{Area} = \frac{1}{2} \cdot 3k \cdot 4k = 6k^2 = 6r^2

📌 The area of the inscribed circle is:

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