tex] ...

August 2022 1 11 Report

Докажите тождество. 10 класс
sin9x+sin10x +sin11x+sin12x=4 cos [tex]\frac{x}{2}[/tex] cos x sin [tex]\frac{21x}{2} [/tex]

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$(sin9x+sin12x)+(sin10x+sin11x)=\\\\=2sin\frac{21x}{2}cos\frac{3x}{2}+2sin\frac{21x}{2}cos\frac{x}{2}=2sin\frac{21x}{2}(cos\frac{3x}{2}+cos\frac{x}{2})=\\\\=2sin\frac{21x}{2}\cdot (2cos2x\cdot cosx)=4sin\frac{21x}{2}\cdot cosx\cdot cos2x$

Здесь угол х/2 не получается.

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