<s>[INST] 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? 
 [/INST] $$\tan x=2\implies \frac{\sin x}2=\frac{\cos x}1\implies \frac{\sin^2x}4=\frac{\cos^2x}1=\frac{\sin^2x+\cos^2x}{4+1}=\frac15$$
$$\frac{\sin^6 x+\cos^6 x}{\sin^4 x+\cos^4 x}=\frac{\left(\frac45\right)^3+\left(\frac15\right)^3}{\left(\frac45\right)^2+\left(\frac15\right)^2}=\frac{(4^3+1)5^2}{5^3(4^2+1)}=\frac{13}{17}$$
</s>