Question

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

Answer 1

Ответ:

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

Пошаговое объяснение:

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