$\begin{align}  & (fog)(x)=f(g(x))={{\sin }^{4}}x-\sqrt{{{\sin }^{4}}x} \\  & ={{\sin }^{4}}x-{{\sin }^{2}}x \\  & \Rightarrow (fog)(x)={{\sin }^{4}}x-{{\sin }^{2}}x={{\sin }^{2}}x({{\sin }^{2}}x-1) \\  & \Rightarrow (fog)(x)=-{{\sin }^{2}}x(1-{{\sin }^{2}}x) \\ \end{align}$ اما $1-{{\sin }^{2}}x={{\cos }^{2}}x$ پس:  $(fog)(x)=-{{\sin }^{2}}x{{\cos }^{2}}x=-{{(\sin x\cos x)}^{2}}$ از آنجایی که $\sin 2x=2\sin x\cos x$ پس: $(fog)(x)=-{{\left( \frac{1}{2}\sin 2x \right)}^{2}}=\frac{-1}{4}{{\sin }^{2}}2x$