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!