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hewwo @hewwo

August 2022 1 11 Report

Найдите значение выражения. 20 баллов!
[tex]\sqrt{2}- 2\sqrt{2}sin^2\frac{15\pi }{8}[/tex]

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Helper211

Ответ: 1

Объяснение:

$2sin^2x=1-cos2x\\\\2sin^2{\frac{15\pi}{8} }=1-cos{\frac{30\pi}{8} }=1-cos{\frac{15\pi}{4} }=1-cos{\frac{15-8\pi}{4}}=1-\frac{\sqrt{2} }{2} \\\\\sqrt{2}-\sqrt{2}\cdot (1-\frac{\sqrt{2} }{2})=\sqrt{2}-\sqrt{2}+\frac{\sqrt{2}\sqrt{2} }{2}=1$

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