i am asked two similar problems. my question is how it was done as the example in the book i am reading is useless in explaining.

the first question is:

(sin^3t+cos^3t)/(sint+cost)=1-sint cost

the example plays out to what i assume is factoring sint+cost out of it to look like (sint+cost)(sin^2t-sint cost+cos^2)/(sint+cost)

my question is, where did the "sin^2t-sint cost+cos^2" come from? when i factor it it doesnt look like that.

the next problem is (cos^4t-sin^4t)/(cos[2t]) how do i get rid of the ^4?

thanks for any help provided.