[tex] \frac{1-8cos^2 \frac{ \alpha }{2}*sin^2 \frac{ \alpha }{2} }{cos3 \alpha +cos \alpha }*(2cos^2 \frac{ \alpha }{2}-1)[/tex]. Created by Ладушки123. algebra-ru

tex]...

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$\frac{1-8Cos^2 \frac{x}{2}*Sin^2 \frac{x}{2}}{Cos3x+Cosx}*(2Cos^2 \frac{x}{2}-1)=$

$= \frac{1-2(2Cos \frac{x}{2}Sin \frac{x}{2})^2}{4Cos^3x-3Cosx+Cosx}*(2( \frac{1+Cosx}{2})-1))=$

$= \frac{1-2Sin^2x}{2Cosx*(2Cos^2x-1)}*Cosx=$

$= \frac{1-2Sin^2x}{2(2Cos^2x-1)}= \frac{Cos2x}{2(2* \frac{1+Cos2x}{2}-1)}=$

$= \frac{Cos2x}{2(1+Cos2x-1)}= \frac{Cos2x}{2(Cos2x)}= \frac{1}{2}$

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