Найти область значений функции y = cos(x)/((cos(x/2)-sin(x/2)). Created by down. matematika-ru

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Найти область значений функции

y = cos(x)/((cos(x/2)-sin(x/2))

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sedinalana Y=(cos²(x/2)-sin²(x/2))/(cos(x/2)-sin(x/2))=
=(cos(x/2)+sin(x/2))(cos(x/2)-sin(x/2))/(cos(x/2)-sin(x/2)=
=cos(x/2)+sin(x/2)=sin(π/2-(x/2))+sin(x/2)=
=2sinπ/4cos(π/4-(x/2))=2*√2/2cos(π/4-(x/2))=√2cos(π/4-(x/2)
E(y)∈√2*[-1;1]=[-√2;√2]
Ответ [-√2;√2]

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