OPGAVEN
 
   
1. Toon aan dat  sin2(α + 1/4π) = 1/2 + sinαcosα
   
   
OPLOSSING
1. sin2(α + 1/4π)
= sin(α + 1/4π) • sin(α + 1/4π)
= (sinαcos1/4π + cosαsin1/4π) • (sinαcos1/4π + cosαsin1/4π)
= sin2α•cos21/4π  + 2sinα•cos1/4π•cosα•sin1/4π + cos2α•sin21/4π
= sin2α • (1/2√2)2 + 2sinαcosα • 1/2√2 • 1/2√2 + cos2α • (1/2√2)2
= 1/2sin2α + sinαcosα + 1/2cos2α
= 1/2(sin2α + cos2α) + sinαcosα
= 1/2 + sinαcosα