Function $x=A{\sin }^2\omega t+B{\cos }^2\omega t+C\sin \omega t\cos \omega t$ represents SHM

The  given equation is 
$x=A{\sin }^2\omega t+B{\cos }^2\omega t+C\sin \omega t\cos \omega t$
Rearraning the equations inqa meaningful from (for interseption of SHM) 
$x=\frac{A}{2}\left(2{\sin }^2\omega t\right)+\frac{B}{2}\left(2{\cos }^2\omega t\right)+\frac{C}{2}\left(2\sin \omega t\cos \omega t\right)$
$=\frac{A}{2}[1-\cos 2\omega t]+\frac{B}{2}[1+\cos 2\omega t]+\frac{C}{2}\sin \left(2\omega t\right)$
The above equation is that of SHM with amplitude  $\frac{C}{2}$  
And angular frequency $2\omega$  
b) If A=B and c=2B then x=B+B sin $2\omega t$ 
This is equation of SHM. The mean position of the  particle executing SHM is  not at the origin.  
C  A=-B, C=2B;  Therefore
$x=B\cos 2\omega t+B\sin 2\omega t$
Let B= $X\cos \varphi =X\sin \varphi$ Then  
$x=X\sin 2\omega t\text{\hspace{0.17em}}\cos \varphi +X\cos 2\omega t\sin \varphi$
This  represents equation of SHM.
d) A=B, C=0 and x=A.  This equation does not represents  SHM