sin^2(pi/4+x)=sin2x+1. Created by WayneFlow. matematika-ru

Ответ:Пошаговое объяснение:

4+x)=sin2x+1...

WayneFlow @WayneFlow

July 2022 1 3 Report

sin^2(pi/4+x)=sin2x+1

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igorShap

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Ответ:

$x=-\dfrac{\pi}{4}+\pi n,n\in Z$

Пошаговое объяснение:

$sin^2\left(\dfrac{\pi}{4}+x\right)=sin2x+1\\ \dfrac{1}{2}\left(1-cos\left(2\cdot\left(\dfrac{\pi}{4}+x\right)\right)\right)=sin2x+1\\ \dfrac{1}{2}\left(1-cos\left(\dfrac{\pi}{2}+2x\right)\right)=sin2x+1\\ \dfrac{1}{2}\left(1-\left(-sin2x\right)\right)=sin2x+1\\ \dfrac{1}{2}\left(1+sin2x\right)=sin2x+1\\ sin2x=-1\\ 2x=-\dfrac{\pi}{2}+2\pi n,n\in Z\\ x=-\dfrac{\pi}{4}+\pi n,n\in Z$

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WayneFlow Откуда взялось 1/2(1-cos(2*(pi/4+x)))?

igorShap Формула понижения степени/половинного аргумента

igorShap sin^2(alpha/2)=(1-cos(alpha))/2

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