Question

cos15°-sin15°/cos15°+sin15°=

Answer 1

cos30°=(cos15°)^2-(sin15°)^2
=(cos15°+sin15°)(cos15°-sin15°)
即：cos15°+sin15°=√3(cos15°-sin15°)/2
所以：
(cos15°-sin15°)/(cos15°+sin15°)
=(cos15°-sin15°)/[√3(cos15°-sin15°)/2]
=2√3/3

Answer 2

(cos15°-sin15°)/(cos15°+sin15°)
=(1-tan15)/(1+tan15)

tan30=(2tan15)/(1-tan15tan15)=√3/3
tan15=2-√3
原式=[1-(2-√3)]/[1+(2-√3)]
=(1-2+√3)/(3-√3)
=√3/3