1 − 2.cos 2x + cos2 2x
kan ook geschreven
worden als
|
A. 1 |
|---|
| B. 2.cos2 x |
| C. 4.cos4 x |
| D. 4.sin4 x |
| E. 4.sin2 x |
[ 5-6781 - op net sinds 16.12.11-(E)-30.10.2023 ]
Translation in E N G L I S H
1 − 2(cos 2x) + cos2 2x
can also be written as
|
A. 1 |
|---|
| B. 2(cos2 x) |
| C. 4(cos4 x) |
| D. 4(sin4 x) |
| E. 4(sin2 x) |
Oplossing - Solution
1ste manier :
1 − 2.cos 2x + cos² 2x = 1 − cos 2x − cos 2x + cos² 2x = 2sin² x − cos 2x (1 − cos 2x)
= 2sin² x − cos 2x.2sin² x = 2sin² x(1 − cos 2x) = 2sin² x. 2sin² x = 4 sin4 x
2de manier : ( 'eleganter' )
1 − 2.cos 2x + cos² 2x = (1 − cos 2x)² = (2sin² x)2 = 4 sin4 x
