Double Angle Formulas

[mathematician]

Hello everyone,

My name is Mathematician, I just joined this posting board, hope I can have something to offer to this community. I need help with a single Trig problem, I have tried to use a proccess of elimination to be able to find the answer, but so far I am breaking a lot of the rules that I am used to in algebra. This problem appears in a calculus book that I am reading by the teacher Mr. W. Michael Kelly. The problem involves in particular, Double- Angle formulas so here is the problem:

"Factor and simplify the expression 2sin x cos x - 4sin^3 x cos x" Now the answer that he came up with

sin 2x cos 2x

(I know its extremely bad to look back at the answers, especially for us mathematicians/teachers) I just need help to try and see how in the world he came up with the answer. His explenation is at the back of the book. "Factor out the greatest common factor of 2sin x cos x to get 2sin x cos x (1-2sin^2x) and use the double angle formulas to substitute in replacments for each factor." And thats his explanation, if any one could provide some pointers, or help walk me through some alternatives, it would be greatly appreciated.

Thanks,

Mathematician (aka Jason)

 

[Deleted member 4993]

Hello everyone,

My name is Mathematician, I just joined this posting board, hope I can have something to offer to this community. I need help with a single Trig problem, I have tried to use a proccess of elimination to be able to find the answer, but so far I am breaking a lot of the rules that I am used to in algebra. This problem appears in a calculus book that I am reading by the teacher Mr. W. Michael Kelly. The problem involves in particular, Double- Angle formulas so here is the problem:

"Factor and simplify the expression 2sin x cos x - 4sin^3 x cos x" Now the answer that he came up with

sin 2x cos 2x

(I know its extremely bad to look back at the answers, especially for us mathematicians/teachers) I just need help to try and see how in the world he came up with the answer. His explenation is at the back of the book.

"Factor out the greatest common factor of 2sin x cos x

to get 2sin x cos x (1-2sin^2x) and

use the double angle formulas to substitute in replacments for each factor."

And thats his explanation, if any one could provide some pointers, or help walk me through some alternatives, it would be greatly appreciated.

Thanks,

Mathematician (aka Jason)

That is a very good explanation -

what part of that explanation is not clear to you?

I assume you are familiar with factoring out greatest common factors

and the double angle formula that the explanation referred to.