a-maths~~~~~

y = 1 – 2sin2x + 4cosx

y = 1 – 2(1 – cos2x) + 4cosx

y = 2cos2x + 4cosx – 1

y = 2[cos2x + 2cosx(1) + 12] – 2 – 1

y = 2(cosx + 1)2 – 3

-1 ≦ cosx ≦ 1

So, when cosx = -1

y attains minimum

ymin = 0 – 3 = -3

when cosx = 1

y attains maximum

ymax = 2(1 + 1)2 – 3

= 2(2)2 – 3

= 5