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Home » Excel Hack You Need: Count Text Data Without Even Looking! - Anadea

Excel Hack You Need: Count Text Data Without Even Looking! - Anadea

📅 May 14, 2026 👤 scraface

May 14, 2026

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📌 The angle between two unit vectors $ \mathbf{u} $ and $ \mathbf{v} $ is given by $ \cos heta = \mathbf{u} \cdot \mathbf{v} $. So,

📌 \cos(lpha - eta) = rac{1}{3}.

📌 We are given $ lpha + eta = 90^\circ $, so $ eta = 90^\circ - lpha $. Substituting,

📌 \cos(lpha - (90^\circ - lpha)) = \cos(2lpha - 90^\circ) = rac{1}{3}.

📌 Using the identity $ \cos(90^\circ - x) = \sin x $, but here we use:

📌 \cos(2lpha - 90^\circ) = \sin(2lpha),

📌 since $ \cos(90^\circ - x) = \sin x $, but sign depends on identity:

📌 \cos(2lpha - 90^\circ) = \cos(90^\circ - 2lpha) = \sin(2lpha) \quad ext{(since } \cos(90^\circ - x) = \sin x ext{)}.

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