Question

(sin7+cos15sin8)/(cos7-sin15sin8)=?

Answer 1

原式=（sin（15-8）+cos15sin8）/（cos（15-8）-sin15sin8）
=（sin15cos8-cos15sin8+cos15sin8）/（cos15cos8+sin15sin8-sin15sin8）
=sin15cos8/cos15cos8
=sin15/cos15
=tan15
=2 - √¯3

至于tan15这里应该是tan15°吧，如果是弧度的话就不对了，如果是弧度只需要写到倒数第二步
cos30 °= √¯3/2
cos15 °= √¯[(1 + cos30° )/2]
sin15° = √¯[(1 - cos30° )/2]
tan15° = sin15° /cos15°
= √¯[(1 - cos30° )/(1 + cos30° )]
= √¯[(2 - √¯3)/(2 + √¯3)]
= (2 - √¯3)

Answer 2

(sin7+cos15sin8)/(cos7-sin15sin8) =(sin(15-8)+cos15sin8)/(cos(15-8)-sin1 5sin8) =(sin15cos8-cos15sin8+cos15sin8)/(co s15cos8+sin15sin8-sin15sin8) =sin15cos8/cos15cos8 =sin15/cos15 =2sin15cos15/2cos²15 =sin30/(1+cos30) =2-√3

Answer 3

(sin7+cos15sin8)/(cos7-sin15sin8)
=(sin(15-8)+cos15sin8)/(cos(15-8)-sin15sin8)
=(sin15cos8-cos15sin8+cos15sin8)/(cos15cos8+sin15sin8-sin15sin8)
=sin15cos8/cos15cos8
=sin15/cos15
=2sin15cos15/2cos²15
=sin30/(1+cos30)
=2-√3