# Prove Trig Identity

• Feb 28th 2014, 04:35 PM
JoeHus
Prove 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 PM
Plato
Re: Prove Trig Identity
Quote:

Originally Posted by JoeHus
Prove cot z -32 cot 32 z = - log cos16 z x cos 8 z x cos 4z x co2z x cos z

As far as I can tell, your post is completely meaningless,
You need to tell us if z is a complex variable?
Do you know the definition of the complex function \$\cot(z)~?\$
• Apr 15th 2014, 06:06 AM
JoeHR
Re: 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