Now, when in doubt, turn everything into sines and cosines:
Now here's the trick. You would typically think that something like can't be simplified as it is the sum of two even powers. However if you do the long division:
But , so the line above really reads:
This is a nice little trick to have in your back pocket.
The problem that I'm having is combining those 2 fractions. Should I multiply them by their reciprocal? If so, after I do that, I would have to make the bases the same and that's were it gets a little confusing. So, if you don't mind explaining how to get the answer from the line I gave or is that a lost cause? Thanks in advance.
After this line:
Then I tried to make the bases the same by multiplying the first side by sin^3x then the other side by cos^3x. This is where I'm really confused, I got:
I don't know if that is right. If so, I just can't figure out how to go any further from here.
This should speak for itself except for one non-standard step. When I was working to cancel the term on the second line I chose to multiply by rather than the "traditional" choice of that we would normally use in the long division. Why? Because it worked.