Question

Найдите область значений функции y= 2/sin^4x+cos^4x

Answer 1

$sin^4x=(sin^2x)^2={1over4}(1-cos2x)^2\cos^4x=(cos^2x)^2={1over4}(1+cos2x)^2\\sin^4x+cos^4x={1over4}(2+2cos^22x)={1over4}(2+cos4x+1)={1over4}(cos4x+3)\\{2over sin^4x+cos^4x}={8over cos4x+3}\\cos4xin[-1;1]\\{2over sin^4x+cos^4x}in[2;4]$