Докажите тождество sin10sin20sin70sin80=(1/4)cos50cos70

Question

Докажите тождество
sin10sin20sin70sin80=(1/4)cos50cos70

Answer 1

Sin 10 = cos 80
sin 20 = cos 70
cos80·sin80·cos70·sin70 = 0.25 cos50·cos70
0.5sin160 · 0.5sin140 = 0.25 cos50·cos70
0.25 sin (90 + 70) · sin (90 + 50) = 0.25 cos50·cos70
0.25 cos50·cos70 ≡ 0.25 cos50·cos70
тождество доказано