Hi everyone, so this is an example from my Calculus for physicists exam that I can't seem to solve.
Prove using Euler's formulae that:
[MATH]tan4\varphi = \frac{4tan\varphi - 4tan^3\varphi}{1-6tan^2\varphi+tan^4\varphi}[/MATH]
It is also written as a hint that we should regard the reciprocal value of the expression, and that tanx=sinx/cosx.
I've done two similair examples which with cot2φ and tan2φ using euler's formulae, but both of those included a specific trick in a specific part of the example which makes it hard to intuitively guess where'd it go in this one.
I have found a couple of videos doing the proof for this expressions, but none of them are using the euler formulae.
Prove using Euler's formulae that:
[MATH]tan4\varphi = \frac{4tan\varphi - 4tan^3\varphi}{1-6tan^2\varphi+tan^4\varphi}[/MATH]
It is also written as a hint that we should regard the reciprocal value of the expression, and that tanx=sinx/cosx.
I've done two similair examples which with cot2φ and tan2φ using euler's formulae, but both of those included a specific trick in a specific part of the example which makes it hard to intuitively guess where'd it go in this one.
I have found a couple of videos doing the proof for this expressions, but none of them are using the euler formulae.
