A Telescoping Tangent Sum

★ 7/10trigonometry Trigonometric Identities Telescoping

Problem

Given $\tan 4x = \dfrac{\sqrt3}{3}$ , evaluate

\frac{\sin 4x}{\cos 8x\cos 4x} + \frac{\sin 2x}{\cos 4x\cos 2x} + \frac{\sin x}{\cos 2x\cos x} + \frac{\sin x}{\cos x}.

Answer

Solution

Difficulty	7/10
Topics	trigonometry, Trigonometric Identities, Telescoping

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