[tex]\bf [sin(x)-1][sin(x)+cos^2(x)]\\\\
-------------------------------\\\\
sin^2(x)+sin(x)cos^2(x)-sin(x)-cos^2(x)
\\\\\\\
[sin^2(x)-cos^2(x)]+[sin(x)cos^2(x)-sin(x)]
\\\\\\
-[cos^2(x)-sin^2(x)]-[sin(x)-sin(x)cos^2(x)]
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-[\stackrel{cos(2x)}{cos^2(x)-sin^2(x)}]-sin(x)\stackrel{sin^2(x)}{[1-cos^2(x)]}
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-cos(2x)-sin(x)sin^2(x)\implies -cos(2x)-sin^3(x)[/tex]
