Interesting trig problem

happybeans

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May 3, 2018
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Can someone plese guide me through this particular problem. I know I have to use defactorisation, but I am not sure how. This is the solution:
trig_problem_1.jpg
 
Can someone plese guide me through this particular problem. I know I have to use defactorisation, but I am not sure how. This is the solution:
View attachment 9874
View attachment 9874
You need to use: (assuming A, B and G are the angles of a triangle)

A + B + G = 180 and cos(180-x) = -cos(x)

Please share your work with us ...even if you know it is wrong.

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/for
 
Can someone plese guide me through this particular problem. I know I have to use defactorisation, but I am not sure how. This is the solution:

Please state the actual problem, not just the solution. It is not clear what is given and what the goal is. The final result does not look like something I would be trying to obtain!

I suppose you are asking for the reasoning in each step? Which steps do you already understand, and which do you need help with?

And what does "defactorisation" mean? The term is not one I have used. But a search shows that it must mean what I know as "product-to-sum identities". One of those is used to obtain the second line; if you don't see that, please list the defactorisation identities you have learned.

To get the third line, you need to use the fact (which you didn't state) that the angles are the angles of a triangle.

The fourth line seems to be a creative rearrangement of terms; I can't see how you would think of it (perhaps you have learned some specific techniques that would motivate it), but it does lend itself to the next line, where they seem to have skipped several steps that might be thought of as rewriting x(1-x) in "vertex form", or as completing the square.

But since I don't know what the goal was, I don't know why they did any of this!
 
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