两个数学问题（要求解答详细）

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