How do you rewrite (sin x - cos x)(sin x + cos x)? Thank you.
You're probably used to dealing with this only in quadratics, but the expression is in the difference of squares pattern
We can just plug in our values for
Which can be rewritten as
If you don't believe me, we can FOIL this expression to make sure:
With FOIL, we multiply the first, outside, inside and last terms and add the result. Thus, we have:
- First terms:
- Outside terms:
- Inside terms:
- Last terms:
Now we have
The middle terms obviously cancel out, and we can rewrite this as
The key realization is that the original expression in question was in a difference of squares pattern.
If you have a
Hope this helps!
Reminder of trig identity: