How do you simplify #sqrt((1-costheta)(1+costheta))#?
2 Answers
It is
where
We used the fact that
Explanation:
For this problem, we can use the difference of squares methods, which tells us that
Applying this method, we then get
Also note that
Thus we can simplify this even further, giving us
We have to be careful here, because the root implies that we should have to answers. In fact, if we would have made the mistake of saying that
Graph of
graph{sqrt(sin x * sinx) [-5.504, 5.596, -2.153, 3.396]}
Graph of
graph{sin x [-5.504, 5.596, -2.153, 3.396]}
These functions are noticeably different, but they're only off by a little bit. In this problem, we could say that