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\frac{\tan(x)-2\sin(x)}{2}
Factor out \frac{1}{2}.
\sin(x)\left(\frac{1}{\cos(x)}-2\right)
Consider \tan(x)-2\sin(x). Factor out \sin(x).
\frac{\sin(x)\left(\frac{1}{\cos(x)}-2\right)}{2}
Rewrite the complete factored expression.