請教一題三角函數

\(\begin{align}
  & \frac{1}{2}bc\sin A={{a}^{2}}-{{\left( b-c \right)}^{2}}={{b}^{2}}+{{c}^{2}}-2bc\cos A-{{\left( b-c \right)}^{2}}=2bc-2bc\cos A \\
& \sin A+4\cos A=4 \\
& {{\sin }^{2}}A+{{\cos }^{2}}A=1 \\
\end{align}\)
解聯立