Упростить [tex]\frac{1+sin2 \alpha}{sin \alpha +cos \alpha } [/tex]. Created by invact. algebra-ru

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Упростить [tex]\frac{1+sin2 \alpha}{sin \alpha +cos \alpha } [/tex]

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$\frac{1+sin2a}{sina+cosa}=\frac{(sina+cosa)^2}{sina+cosa}=sina+cosa\\
$
так как $(sina+cosa)^2=sin^2+cos^2a+2sinacosa=1+sin2a$

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Светланаskrip $\frac{1+sin2a}{sina+cosa}= \\ \\ \frac{1+2sinacosa}{sina+cosa}= \\ \\ \frac{sin^{2}a+cos^{2}a+2sinacosa}{sina+cosa}= \\ \\ \frac{sin^{2}a+2sinacosa+cos^{2}a}{sina+cosa} \\ \\ (sin^{2}a+2sinacosa+cos^{2}a=(sina+cosa)^{2}) \\ \\ \frac{(sina+cosa)^{2}}{sina+cosa}=sina+cosa$

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