我在書上看到的過程,不太明白:cosA = cos(A/2)^2 - sin(A/2)^2 = (1-tg(A/2)^2)/((1+tgA/2)^2)

熱心網(wǎng)友

cosA=cos(A/2+A/2)=cos(A/2)cos(A/2)-sin(A/2)sin(A/2)=cos(A/2)^2 - sin(A/2)^2=cos(A/2)^2*[1-tan(A/2)^2]=[1-tan(A/2)^2]/sec(A/2)^2=(1-tan(A/2)^2)/((1+tan(A/2)^2).

熱心網(wǎng)友

你看到過倍角公式嗎？你看到過cos2A = cos(A)^2 - sin(A)^2 = (1-tg(A)^2)/(1+tg(A)^2)嗎？你如果看過，你就能理解：cosA = cos(A/2)^2 - sin(A/2)^2 = (1-tg(A/2)^2)/(1+tg(A/2)^2)

熱心網(wǎng)友

cosA = cos(A/2)^2 - sin(A/2)^2，(倍角公式）= [cos(A/2)^2 - sin(A/2)^2]/[cos(A/2)^2 + sin(A/2)^2]，（分母 = 1）= [1 - tg(A/2)^2]/[(1 + tg(A/2)^2]，[分子、分母同除以：cos(A/2)^2]