Question

cos(π/4+α)*sinα. формула sinα*cosβ=1/2[sin⁡(α+β]+sin⁡(α-β)

Answer 1

$cos(\frac{\pi}{4}+ \alpha )\cdot sin \alpha =\frac{1}{2}(sin((\frac{\pi}{4}+\alpha )+\alpha )+sin( \alpha -(\frac{\pi}{4}+ \alpha ))= \\\\=\frac{1}{2}(sin(\frac{\pi}{4}+2 \alpha )+sin(-\frac{\pi}{4}))=\frac{1}{2}(sin(\frac{\pi}{4}+2 \alpha )-\frac{\sqrt2}{2})$