Prove

cot z -32 cot 32 z = - log cos16 z x cos 8 z x cos 4z x co2z x cos z

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- Feb 28th 2014, 04:35 PMJoeHusProve Trig Identity
Prove

cot z -32 cot 32 z = - log cos16 z x cos 8 z x cos 4z x co2z x cos z - Feb 28th 2014, 04:44 PMPlatoRe: Prove Trig Identity
- Apr 15th 2014, 06:06 AMJoeHRRe: Prove Trig Identity
Sorry for not replying as I lost my details due to a computer crash.

Z is not a complex variable and yes I do know the definition of the complex function cot Z.

The above identity was from an exam question for A-Levels passed to me and the full context of the question was

Prove

tan z + 2 tan2z + 4 tan4z +8 tan8z + 16tan16z=cot z -32 cot 32 z

I only posted part of the question which included a hint from someone: to work on right hand side by integrating it and expanding it to - log cos16 z x cos 8 z x cos 4z x co2z x cos z and finally differentiating it.

The differentiation part is easy and immediately results in the left hand side answer, no problem.

Integrating results in a ln sinz etc , but the expansion is not so easy.

regards

JoeHR