Question

ВЫРУЧАЙТЕ,СРОЧНО найти область значений

Answer 1

$f(x)= \frac{1}{sin^4x+cos^4x} = \frac{1}{(sin^2x+cos^2x)^2-2sin^2x \cdot cos^2x} =\frac{1}{1-\frac{1}{2}sin^22x}\\\\0 \leq sin^22x \leq 1\\\\0 \leq \frac{1}{2}sin^22x \leq \frac{1}{2}\; ,\; \; -\frac{1}{2} \leq -\frac{1}{2}sin^22x \leq 0\\\\\frac{1}{2} \leq 1-\frac{1}{2}sin^22x \leq 1\\\\1 \leq \frac{1}{1-\frac{1}{2}sin^22x} \leq 2\\\\f(x)\in [\, 1,2\, ]$