Предмет: Алгебра, автор: Anastastasiya

1+sin2x=(sin2x-cos2x)^2 решить уравнение..помогите пожалуйста,только подробно^^

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Автор ответа: Аноним

$1+sin2x=(sin2x-cos2x)^{2}\ 1+sin2x=sin^{2}2x-2sin2x*cos2x+cos^{2}2x\ 1+sin2x=1-2sin2x*cos2x\ sin2x+2sin2x*cos2x=0\ sin2x(1+2cos2x)=0\ 1)sin2x=0\ 2x=pi n\ x=frac{pi n}{2}\ 2)1+2cos2x=0\ 2cos2x=-1\ cos2x=-frac{1}{2}\ 2x=pmfrac{2pi}{3}+2pi n\ x=pmfrac{pi}{3} + pi n,n in mathbb{Z}$

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