The Purplemath Forums

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-sin...

I factored wrong. i found that (cos^4t-sin^4t) is the same as saying (cos^2t+sin^2t)(cos^2t-sin^2t) one of which is a Pythagorean identity. the lower part of the problem, Cos(2t) is part of a series of identities which which cancels one half of the upper part of the equation. meaning you are left is...