cos75°-sin75°除以 cos75°+ sin75°

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cos75°-sin75°除以 cos75°+ sin75°
cos75°-sin75°除以 cos75°+ sin75°

cos75°-sin75°除以 cos75°+ sin75°
分子分母同乘(cos75-sin75)
原式=(cos75-sin75)²/(cos+sin75)(cos75-sin75)
=(cos²75+sin²75-2sin75cos75)/(cos²75-sin²75)
=[1-sin(2*75)]/cos(2*75)
=(1-sin150)/(cos150)
=(1-1/2)/(-√3/2)
=-√3/3

(cos75°-sin75°)/(cos75°+sin75°)
=(cos75°-sin75°)^2/[(cos75°+sin75°)(cos75°-sin75°)]
=(1-2sin75°cos75°)/(cos^275°-sin^275°)
=(1-sin150°)/cos150°
=(1-sin30°)/(-cos30°)
=(1-1/2)/(-√3/2)
=-√3/3