Verifying Trigonometric Identities Help

[Mystogan]

So this is one of my problems for homework and I just keep getting stuck when trying to solve it.

\(\displaystyle \dfrac{\cos^3(x)\, +\, \sin^3(x)}{\cos(x)\, -\, \cos^2(x)\sin(x)}\, =\, 1\, +\, \tan(x)\)

Basically I start off by taking the 'cosx' out of the denominator so it looks like 'cosx(1-cosxsinx)', but i'm not getting anywhere with it. Could someone tell me if this is the first step I should be taking, and if not, guide me to the first step so I can solve it? Thanks

 

[stapel]

I just keep getting stuck when trying to solve it.

\(\displaystyle \dfrac{\cos^3(x)\, +\, \sin^3(x)}{\cos(x)\, -\, \cos^2(x)\sin(x)}\, =\, 1\, +\, \tan(x)\)

Basically I start off by....

A description of "basically" what you do does not help us troubleshoot. Kindly please reply with a clear listing of your steps so far. Thank you!

 

[Deleted member 4993]

So this is one of my problems for homework and I just keep getting stuck when trying to solve it.

\(\displaystyle \dfrac{\cos^3(x)\, +\, \sin^3(x)}{\cos(x)\, -\, \cos^2(x)\sin(x)}\, =\, 1\, +\, \tan(x)\)

Basically I start off by taking the 'cosx' out of the denominator so it looks like 'cosx(1-cosxsinx)', but i'm not getting anywhere with it. Could someone tell me if this is the first step I should be taking, and if not, guide me to the first step so I can solve it? Thanks

Hint:

a³ + b³ = (a + b)(a² -a*b + b²)