Code:
\[ \begin{eqnarray*}\frac{\cos x}{\sin x}+\frac{\sin x}{1+\cos x}&=&\frac{\cos x+\cos^{2}x+\sin^{2}x}{\sin x(1+\cos x)}\\ &=&\frac{\cos x+1}{\sin x(1+\cos x)}\\ &=&\frac{1}{\sin x}\\ &=&\csc x\end{eqnarray*} \]
Code:
\[ \begin{eqnarray*}\frac{\cos x}{\sin x}+\frac{\sin x}{1+\cos x}&=&\frac{\cos x+\cos^{2}x+\sin^{2}x}{\sin x(1+\cos x)}\\ &=&\frac{\cos x+1}{\sin x(1+\cos x)}\\ &=&\frac{1}{\sin x}\\ &=&\csc x\end{eqnarray*} \]
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