Question

Упростить:
sin20cos40+cos20sin40
sin45cos15-cos45sin15

Answer 1

sin(α+β) = sin(α)·cos(β) + sin(β)·cos(α)
sin(α-β) = sin(α)·cos(β) - sin(β)·cos(α)

sin20cos40 + cos20sin40 = sin(20+40) = sin 60 = √3/2
sin45cos15 - cos45sin15 = sin (45 - 15) = sin 30 = 1/2