Предмет: Алгебра, автор: МайклВегвиц

помогите, очень нужна помощь, сижу над этим уравнением уже час

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Автор ответа: kalbim

0

$sin^{2}(x+ \frac{3 \pi }{2})+0.5*sin(2x)=1$
$cos^{2}x+0.5*2*sinx*cosx=sin^{2}x+cos^{2}x$
$sinx*cosx-sin^{2}x=0$
$sinx*(cosx-sinx)=0$
1) $sinx=0$
$x= \pi k$ , k∈Z
2) $sinx=cosx$
$tgx=1$
$x= \frac{ \pi }{4}+ \pi k$ , k∈Z

Использовала формулы:
1) приведения: $sin(x+ \frac{3 \pi }{2})=-cosx$
$sin^{2}(x+ \frac{3 \pi }{2})=(-cosx)^{2}=cos^{2}x$
2) двойного угла синуса: $sin(2x)=2*sinx*cosx$
3) основное тригонометрическое тождество: $1=sin^{2}x+cos^{2}x$

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