两个数学问题（要求解答详细）

两个数学问题（要求解答详细）
1.sin50度(1+√3 tan10度）=?
2.sin7度+cos15度sin8度/cos7度-sin15度sin8度=?

1.sin50°[1+(√3)×tan10°]
=sin50×[(√3)sin10+cos10]/cos10
=(sin50/cos10)×2×(cos30sin10+cos10sin30)
=(sin50/cos10)×2×sin40
=2×sin50×cos50/cos10
=sin100/cos10
=cos10/cos10
=1
2.(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