|
Het product
cos 15° . cos 30° . cos 75°
is gelijk aan
|
A. \(\frac{3}{8}\) |
|---|
| B. \(\frac{\sqrt3}{2}\) |
| C. \(\frac{\sqrt3}{4}\) |
| D. \(\frac{1}{4}\) |
| E. \(\frac{\sqrt3}{8}\) |
[ 5-5711 - op net sinds 13.9.13-(E)-13.6.2025 ]
Translation in E N G L I S H
The product
(cos 15°)(cos 30°)(cos 75°)
is equal to
|
A. \(\frac{3}{8}\) |
|---|
| B. \(\frac{\sqrt3}{2}\) |
| C. \(\frac{\sqrt3}{4}\) |
| D. \(\frac{1}{4}\) |
| E. \(\frac{\sqrt3}{8}\) |
Oplossing - Solution
1ste manier :
cos 15°.cos 30°.cos 75° = sin 15°.cos 15°.cos 30°
= ½.(2 sin 15°.cos 15°).cos 30°
= ½.sin 30°.cos 30° = ¼.2. sin 30°.cos 30°
= ¼ .sin60° = \(\frac 14.\frac {\sqrt3} {2}=... \)
2de manier : (gebruik makend van één van de 4 formules van SIMPSON)
cos 15°.cos 30°.cos 75° = ½.cos30°(2cos 15°.cos 75°)
= ½.cos 30°[cos(15° − 75°) + cos(15° + 75°)]
= ½.cos 30°.[cos(− 60°) + cos 90°]
= ½.cos 30°. ½= ¼ cos 30° = \(\frac14.\frac {\sqrt3} {2}=... \)
