Question

高一 数学 三角恒等变换 请详细解答,谢谢! (29 19:49:26)

（sin7+cos15*sin8)/(cos7+sin15*sin8)
 
“*”为乘

Answer 1

(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

Answer 2

我也按写错了算。
(sin7+cos15sin8)/(cos7-sin15sin8)
=（sin(15-8)+cos15sin8）/(cos(15-8)-sin15sin8)
=sin15cos8/(cos15cos8)
=sin15/cos15
=2sin15*sin15/(2sin15*cos15)
=(1-cos30)/sin30
=2-根3。