sin 15°.sin 30°.sin 45°.sin 60°.sin 75°

is gelijk aan 		A.   \(\boldsymbol{1}\)
B.   \(\boldsymbol{\frac12}\)
C.   \(\boldsymbol{\frac12\sqrt2}\)
D.   \(\boldsymbol{-\frac12\sqrt2}\)
E.   \(\boldsymbol{\frac1{32}\sqrt6}\)
A    B    C    D    E

[ 5-3123 - op net sinds 11.3.16-(E)-4.11.2023 ]

Translation in   E N G L I S H

sin 15°.sin 30°.sin 45°.sin 60°.sin 75°

is equal to 		A.   \(\boldsymbol{1}\)
B.   \(\boldsymbol{\frac12}\)
C.   \(\boldsymbol{\frac12\sqrt2}\)
D.   \(\boldsymbol{-\frac12\sqrt2}\)
E.   \(\boldsymbol{\frac1{32}\sqrt6}\)

Oplossing - Solution

We passen de volgende formule toe :
sin x . sin y = 1op2 [ cos(x − y) − cos(x + y)]
(een minder gebruikte vorm van de formules van SIMPSON)
  sin 15°.sin 30°.sin 45°.sin 60°.sin 75°
= (sin 15°.sin 75°).sin 30°.sin 45°.sin 60°
= [cos(15°−75°)− cos(15°+75°)]. .
= [cos60°− cos90°]. .
=
= 1op34.gif