Verifying (sin³(x)-cos³(x))/(sin(x)-cos(x)) = 1+sin(x)cos(x)

[RAF1940]

(sin^3(x)-cos^3(x))/(sinx-cosx) = 1+(sinx*cosx)


I'm following a path similar to the post on http://www.askmehelpdesk.com/mathematics/verify-identity-sin-3-x-cos-3-x-sin-x-cos-x-1-sin-x-cos-x-500483.html

However, I keep getting 1-(sinx*cosx) when solving for mine as I end up with ((sinx-cosx)(1-sinxcosx))/sinx-cosx

Help, please?

 

[SammyS]

(sin^3(x)-cos^3(x))/(sinx-cosx) = 1+(sinx*cosx)

I'm following a path similar to the post on http://www.askmehelpdesk.com/mathematics/verify-identity-sin-3-x-cos-3-x-sin-x-cos-x-1-sin-x-cos-x-500483.html

However, I keep getting 1-(sinx*cosx) when solving for mine as I end up with ((sinx-cosx)(1-sinxcosx))/sinx-cosx

Help, please?

The identity for the difference of cubes:

a³ - b³ = (a - b)(a² + ab + b²)

 

[lurflurf]

multiply the right hand side by one in the form
$$\frac{\sin(x)-\cos(x)}{\sin(x)-\cos(x)}$$
and use
$$\cos^2(x)+\sin^2(x)=1$$