E-TA01 · One angle equation, two signed progressions
The numbers \(2\sin x\), \(\cos x\), \(-\sin x\) are consecutive AP terms, with \(0\le x<2\pi\).
Obtain an equation for x and show that a solution cannot have \(\cos x=0\).
Find all x exactly and the common difference for each. Let \(\alpha=\tan^{-1}2\).
Each of the resulting APs is continued. Find the sum of its first eight terms, matching the sum to the angle.
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