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Home » The angles of a triangle are in the ratio 2:3:4. Calculate the measure of each angle. - 500apps

The angles of a triangle are in the ratio 2:3:4. Calculate the measure of each angle. - 500apps

📅 March 15, 2026 👤 scraface

Mar 15, 2026

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📌 Thus, the value of \( v \) is \(\boxed{6}\).Question: Determine the maximum value of \((\sec \theta + \csc \theta)^2\) for \(\theta \in (0^\circ, 90^\circ)\).

📌 Solution: To find the maximum value of \((\sec \theta + \csc \theta)^2\), first express it in terms of sine and cosine:

📌 \sec \theta = \frac{1}{\cos \theta}, \quad \csc \theta = \frac{1}{\sin \theta}.

📌 \sec \theta + \csc \theta = \frac{1}{\cos \theta} + \frac{1}{\sin \theta} = \frac{\sin \theta + \cos \theta}{\sin \theta \cos \theta}.

📌 The square is:

📌 Using the identity \((\sin \theta + \cos \theta)^2 = 1 + \sin 2\theta\), and \(\sin \theta \cos \theta = \frac{1}{2} \sin 2\theta\), we rewrite it as:

📌 Let \(y = \sin 2\theta\), where \(y \in (0, 1]\). Define:

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