急！ F4 數學題

The maximum value of cos x and sin x are 1.
Put cos 2x=1 and sin x=1 into (cos 2x)^2 + 2(sin x)^2:
(cos 2x)^2 + 2(sin x)^2
=(1)^2 + 2(1)^2
=1+2
=3
The maximum value of (cos 2x)^2 + 2(sin x)^2 is 3.

The minimum value of cos x and sin x are -1.
Put cos 2x=-1 and sin x=-1 into (cos 2x)^2 + 2(sin x)^2:
(cos 2x)^2 + 2(sin x)^2
=(-1)^2 + 2(-1)^2
=1+2
=3
However, it is the maximum value of (cos 2x)^2 + 2(sin x)^2.
The non-negative minimum value of cos x and sin x is 0.
Hence, we put cos 2x=0 and sin x=0 and we will get:
(cos 2x)^2 + 2(sin x)^2
(0)^2 + 2(0)^2
=0
The minimum value of (cos 2x)^2 + 2(sin x)^2 is 0.

max: 3
min: 0