F.4 附加數學 - 和差化積與積化和差公式

1)L.H.S.
= cos2(π/8﹣A)﹣cos2(π/8 + A)
= [cos(π/8﹣A) + cos(π/8 + A)][cos(π/8﹣A)﹣cos(π/8 + A)]
= [2 cos(π/8) cosA][2 sin(π/8) sinA]
= sin(π/4) sin2A
= (√2/2)sin2A
= R.H.S.

2)L.H.S.
= sin3α sin3 α + cos3α cos3α
= 1/2(cos 2α﹣cos 4α) sin2 α + 1/2(cos2α + cos4α) cos2 α
= 1/2[cos 2α﹣cos 4α(cos2α﹣sin2α)]
= (1/2)(cos 2α + cos 4α cos 2α)
= cos 2α[(1/2)(1+ cos 4α]
= cos 2α(cos22α)
= cos32α
= R.H.S.

Excellent ~

1左方=cos²(π/8 -A)-cos²(π/8 +A)
=[1+cos(π/4 - 2A)]/2 - 1+cos(π/4 + 2A)]/2
=[cos(π/4-2A)-cos(π/4+2A)]/2
=sinπ/4sin2A
=(√2 ∕ 2 )sin2A
=右方