Question

求（sin8°+sin7°cos15°）/（cos8°-sin7°sin15°）的值

Answer 1

（sin8°+sin7°cos15°）/（cos8°-sin7°sin15°）
=(sin(15-7)+sin7cos15)/(cos(15-7)-sin7sin15)
=(sin15cos7-cos15sin7+sin7cos15)/(cos15cos7+sin15sin7-sin15sin7)
=(sin15cos7)/(cos15cos7)
=tan15
tan30=2tan15/(1-(tan15)^2)=根号3/3，由此算出tan15

Answer 2

sin8°+sin7°cos15°
=sin(15°-7°) +sin7°cos15°
=sin15°cos7°-sin7°cos15°+sin7°cos15°
=sin15°cos7°

cos8°-sin7°sin15°
=cos(15°-7°) -sin7°sin15°
=cos15°cos7°+sin7°sin15°-sin7°sin15°
=cos15°cos7°

故
（sin8°+sin7°cos15°）/（cos8°-sin7°sin15°）
=sin15°cos7°/cos15°cos7°
=tan15°