[tex]cos2x+sin^2x=0,75[/tex]. Created by matwej2201. algebra-ru

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matwej2201 @matwej2201

July 2022 1 7 Report

[tex]cos2x+sin^2x=0,75[/tex]

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Воспользуемся формулой связи косинуса двойного угла и синуса угла.

$\cos{2x}+\sin^2{x}=0,75\\1-2\sin^2{x}+\sin^2{x}=0.75\\0.25=\sin^2{x}\\\sin{x}=\pm 0.5\\x=\pm \arcsin{0.5}+\pi k,k\in \mathbb{Z}.\\x=\pm \frac{\pi}{6}+\pi k,k\in \mathbb{Z}.\\\\Otvet\!\!:\;x=\pm \frac{\pi}{6}+\pi k,k\in \mathbb{Z}.$

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