25б!!! Решите: ((sina+sin3a)/(cosa+cos3a))*(1 +cos4a). Created by Gerashine. algebra-ru

(cosa+cos3a))*(1 +cos4a)...

Gerashine @Gerashine

July 2022 1 28 Report

25б!!! Решите:
((sina+sin3a)/(cosa+cos3a))*(1 +cos4a)

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$\frac{Sin\alpha+Sin3\alpha}{Cos\alpha+Cos3\alpha}*(1+Cos4\alpha )=\frac{2Sin\frac{\alpha+3\alpha}{2}*Cos\frac{\alpha-3\alpha}{2}}{2Cos\frac{\alpha+3\alpha}{2}*Cos\frac{\alpha-3\alpha}{2}} *(1+Cos4\alpha)=\\\\=\frac{Sin2\alpha*Cos\alpha}{Cos2\alpha*Cos\alpha} *2Cos^{2}2\alpha=\frac{Sin2\alpha*2Cos^{2}2\alpha}{Cos2\alpha }=2Sin2\alpha Cos2\alpha=\boxed{Sin4\alpha}$

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