[tex]\frac{cos^2\alpha+cos\alpha}{2cos^2\frac{\alpha}{2}}+1[/tex]. Created by abduqodirovaziz. algebra-ru

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[tex]\frac{cos^2\alpha+cos\alpha}{2cos^2\frac{\alpha}{2}}+1[/tex]

alvardsaroyan $\frac{cos^2 \alpha +cos \alpha }{2cos^2\frac{ \alpha }{2}}+1=\frac{cos \alpha (cos \alpha +1)}{1+cos \alpha }+1=cos \alpha +1=2cos^2\frac{ \alpha }{2}\\\\P.S.\; \; \; cos \alpha +1=(cos^2\frac{ \alpha }{2}-sin^2\frac{ \alpha }{2})+(sin^2\frac{ \alpha }{2}+cos^2\frac{ \alpha }{2})=2cos^2\frac{ \alpha }{2}$

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abduqodirovaziz Спасибо!

alvardsaroyan ok

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Verified answer

$\frac{cos \alpha (cos \alpha +1)}{1+cos \alpha } +1=cos \alpha +1$ =2cos² $\frac{ \alpha }{2}$

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abduqodirovaziz Благодарю!

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