You can put this solution on YOUR website!
First, the sum of cubes
This applies to the denominator
but you see the sin squared and cos squared add to 1?
simplify denominator a bit more to get:
Note that
and if we factor a sin out of the first two terms in denominator we get:
and can make the substitution:
Next we have
so let's factor sin out of the later part of denominator
and make the substitution
now, factor out sin in the denominator:
And after canceling numerator/denominator all we have left is
which is cosecant.
There may be a faster or more elegant method, but it's key to see that the sum of two cubes had to be factored to start the process.
