How Can You Factor the Trigonometric Expression sin^3(x)-cos^3(x)?

[xCycLoNeX]

Homework Statement

sin^3(x)-cos^3(x)
sin(x) - cos(x)

equals

1 + sin(x) + cos(x)

Homework Equations

Not sure :/

The Attempt at a Solution

Not sure where to even start.

 

[bp_psy]

Are you sure that it's 1+sin(x)+cos(x) and not 1+sin(x)cos(x)?

Use the identity sin^2(x)+cos^2(x)=1.

 

[xCycLoNeX]

Oh yeah, that was it.

 

[Anakin_k]

sin^3(x)-cos^3(x)
-----------------
sin(x) - cos(x)

Try factoring the numerator, it may help you.