（sin7°+cos15°*sin8°）/(cos7-sin15°*sin8°)答案是2-根号3,求详细过程

（sin7°+cos15°*sin8°）/(cos7-sin15°*sin8°)答案是2-根号3,求详细过程
（sin7°+cos15°*sin8°）/(cos7-sin15°*sin8°)
答案是2-根号3,求详细过程

（sin7°+cos15°*sin8°）/(cos7-sin15°*sin8°)答案是2-根号3,求详细过程
(sin7+cos15sin8)/(cos7-sin15sin8)
=[sin7+cos(7+8)sin8]/[cos7-sin(7+8)sin8]
=[sin7+(cos7cos8-sin7sin8)sin8]/[cos7-(sin7cos8+sin8cos7)sin8]
=(sin7+cos7cos8sin8-sin7sin²8)/(cos7-sin7sin8cos8-sin²8cos7)
=(sin7-sin7sin²8+cos7cos8sin8)/(cos7-sin²8cos7-sin7sin8cos8)
=[sin7(1-sin²8)+cos7cos8sin8]/[cos7(1-sin²8)-sin7sin8cos8]
=(sin7cos²8+cos7cos8sin8)/(cos7cos²8-sin7sin8cos8)
=(sin7cos8+cos7sin8)/(cos7cos8-sin7sin8) {每项除以cos8}
=sin(7+8)/cos(7+8)
=sin15/cos15
=tan15
=tan(45-30)
=[tan45-tan30]/[1-tan45*tan30]
=[1-根号3/3]/(1-根号3/3)
=2-根号(3)