Calculate value of expression $(\sin^6 x+\cos^6 x)/(\sin^4 x+\cos^4 x)$ 
Calculate the value of expresion:
  $$
E(x)=\frac{\sin^6 x+\cos^6 x}{\sin^4 x+\cos^4 x}
$$ 
  for $\tan(x) = 2$.

Here is the solution but I don't know why $\sin^6 x + \cos^6 x = ( \cos^6 x(\tan^6 x + 1)  )$, see this:

Can you explain to me why they solved it like that? 

Since $\frac{\sin x}{\cos x}=\tan x=2$, Simply replace $\sin x$ with $2\cos x$ and see hwo far you get. Then think about ways to express $\cos^2$ with $\tan$.
