1/4*sin(405+b)*cos(b+765)

Question

1/4*sin(405+b)*cos(b+765)

Answer 1

Sin(405° + β) = Sin(360 °+ 45° +β) = Sin(45° + β)
Cos(765°+ β) = Cos(720 °+ 45 +β) = Cos(45° +β)
 Sin(45° + β)*Cos(45° +β)= √2/2(Cosβ + Sinβ) * √2/2 (Cosβ - Sinβ)=
= 1/2 (Cos²β - Sin²β) = 1/2 Cos2β
сам пример: 1/4*1/2*Сos2β = 1/8* Co2β