问一道高中数学题(三角函数)!是一个分式的化简:sin7'+cos15'sin8'---------------------cos7'-sin15'sin8'注:' 是度数.

原式=sin(15'-8')+cos15'sin8'
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cos(15'-8')-sin15'sin8'
=sin15'cos8'-cos15'sin8'+cos15'sin8'
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cos15'cos8'+sin15'sin8'-sin15'sin8'
=sin15'cos8'
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cos15'cos8'
=tan15'

首先：把cos15'sin8' 和sin15'sin8' 用积化和差公式，化简一下：
cos15'sin8'=1/2（sin（15+8）-sin(15-8)）=1/2(sin23-sin7)
sin15'sin8'=-1/2(cos(15+8)+cos(15-8))=-1/2(cos23-cos7)
则原式变成：sin7'+1/2sin23-1/2sin7 1/2sin7+1/2sin23 sin7+sin23
--------------------- = --------------------- =-----------
cos7'+1/2cos23-1/2cos7 1/2cos7+1/2cos23 cos7+cos23

原式=[sin(15-8)+cos15sin8]/[cos(15-8)-sin15sin8]
=(sin15cos8-cos15sin8+cos15sin8)/(cos15cos8+sin15sin8-sin15sin8)
=sin15cos8/cos15cos8
=sin15/cos15
=tan15