Trigonometric identity of finite terms – math.stackexchange.com

Trigonometric identity of finite terms – math.stackexchange.com

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Prove that: $$\dfrac{1}{\cos x+\cos {3x}} + \dfrac{1}{\cos x+ \cos {5x}}+\dots+\dfrac{1}{\cos x+ \cos {(2n+1)x}} \\= \frac{1}{2}\csc x \,[ \tan{(n+1)x}-\tan{x}]$$ I tried to prove this using the ...

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