De minimale waarde van
4.sin
2
x + 8.sin
2
x.cos
2
x + 4.cos
2
x
is
A. 1
B. 12
C. 8
D. 4
E. 6
[ 5-4914 - op net sinds 10.11.14-(E)-27.10.2023 ]
Translation in E N G L I S H
What is the minimum value of
4.sin
2
x + 8.sin
2
x.cos
2
x + 4.cos
2
x
A. 1
B. 12
C. 8
D. 4
E. 6
Oplossing - Solution
4.sin²x + 8.sin²x.cos²x + 4.cos²x
= 2(2sin²x + 2cos²x + 4.sin²x.cos²x)
= 2(2 + sin² 2x)
= 4 + 2.sin² 2x
De minimale waarde van sin²2x is 0, dus van 4 + 2sin2x is dat 4 + 2.0 = ...