verify trig identity

[trigstudent]

need lots of help I have to verify and can't get started. looked in the direction of dbl angle identities and sum difference identities but I am just lost.


sin4x=(cosx)(4sinx-8sin^3x)



AND



tan3x=(3tanx-tan^3x)/(1-3tan^2x)

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[jolly]

need lots of help

Where exactly?

 

[stapel]

I have to verify and can't get started.

A good way to start is to pick the "more complicated" side of the identity (this is often a matter of taste) and start working with that. Try stuff. The first identity has parentheses on the right-hand side. Have you multiplied that out? Have you noticed anything useful that could be extracted?

There is no "formula" for this sort of thing. The point is that you get good at taking things apart, recognizing patterns, substituting, and manipulating.

If you get stuck, please reply showing all of the steps and reasoning you have tried.

Thank you.

Eliz.

 

[galactus]

Your last identity is one of the triple angle formulae. They're more obscure than double angle formulae and are not in most books.

I would use the double angle and addition formulas to prove this.

Start with \(\displaystyle tan(3x)=tan(2x+x)\)

Expand it out using the addition formula. Then expand out tan(2x) using

the double angle formula. It will fall into place with some careful algebra.

The first problem can be done the using the same methods.

Good luck.