求證：cos(a+b)cos(a-b)=(cosa)^2-(sinb)^2

熱心網(wǎng)友

用積化和差公式及半角公式，很容易得到結(jié)果。cos(a+b)cos(a-b)=(1/2)(cos2a+cos2b)=(1/2)[1-2(sina)^2+1-2(sinb)^2]=1-(sina)^2-(sinb)^2=(cosa)^2-(sinb)^2

熱心網(wǎng)友

cos(a+b)cos(a-b)=(cosacosb-sinasinb)(cosacosb+sinasinb)=(cosa)^2(cosb)^2-(sina)^2(sinb)^2=(cosa)^2(1-(sinb)^2)-(1-(cosa)^2)(sinb)^2展開就得出右邊的結(jié)果拉!