Помогите,СРОЧНО,пожалуйста Найти область значений функции у=1/(sin^4(x)+cos^4(x)). Created by pokipoki. algebra-ru

(sin^4(x)+cos^4(x))...

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Помогите,СРОЧНО,пожалуйста
Найти область значений функции
у=1/(sin^4(x)+cos^4(x))

Answers & Comments

Alexandr130398 $sin ^{4} x+cos ^{4} x=sin ^{4} x+cos ^{4} x-2sin ^{2} x*cos ^{2} x+2sin ^{2} x*cos ^{2} x= \\ (sin ^{4} x+2sin ^{2} x*cos ^{2} x+cos ^{4} x)-2sin ^{2} x*cos ^{2} x= \\ (sin ^{2} x+cos ^{2} x) ^{2} -2sin ^{2} x*cos ^{2} x=[tex]y= \frac{1}{sin ^{4} x+cos ^{4} x} \ \textless \ =\ \textgreater \ y= \frac{1}{1- \frac{1}{2} sin ^{2} (2x)} \\ 0\leq sin ^{2} (2x) \leq 1 \\ - \frac{1}{2} \leq - \frac{1}{2} sin ^{2}(2x) \leq 0 \\ \frac{1}{2} \leq 1- \frac{1}{2} sin ^{2} (2x) \leq 1 \\1 \leq \frac{1}{1- \frac{1}{2} sin ^{2} (2x)} \leq 2 \\ E(y)=[1;2]$ [/tex]

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