Question

(Sin7°+cos15°sin8°)÷(cos7°－sin15°sin8°)=?

谢谢拉
希望写过程！

Answer 1

为了表示方便我就不写°了直接用数字表示度数,虽然这样不规范.
(sin7+cos15sin8)/(cos7-sin15sin8)
====积化和差
=[sin7+(sin23-sin7)*0.5]/[cos7+(cos23-cos7)*0.5]
=(0.5sin7+0.5cos23)/(0.5cos7+0.5cos23)
====约分,和差化积
=(sin15*sin8)/(cos15*cos8)
====约分
=tan15(即tg15,我不知道你习惯用那种方式表示 正切)
====半角公式
=(1-cos30)/sin30
=2-3^(1/2) 就是2-根号3

Answer 2

=(sin(15-8)+cos15sin8)/(cos(15-8)-sin15sin8=(sin15cos8-cos15sin8+cos15sin8)/(cos15sin8+sin15cos8-sin15sin8)=sin15/cos15=tan15=tan(45-30)=2-根3

Answer 3

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)请点击
采纳为答案