Question

高三数学拜托~~~y=(6cos^4x+5sin²x-4）/cos2x的值域

Answer 1

y=(6cos^4x+5sin²x-4）/cos2x

=(6cos^4x+5-5cos²x-4)/(2cos²x-1)

=(6cos^4x-5cos²x+1)/(2cos²x-1)

=(2cos²x-1)(3cos²x-1)/(2cos²x-1)

=3cos²x-1

=3(cos2x+1)/2-1

=(3cos2x)/2+1/2

当cos2x=1时,ymax=4

当cos2x=-1时,ymin=-1