Question

求sin45cos30＋cos45sin30／cos45cos30－sin45sin30的值，要有详细的过程，有公式和文字说明更好了！

我是刚学，请阐述简单一点！

Answer 1

sinAcosB+cosAsinB=sin(A+B)
sinAcosB-cosAsinB=sin(A-B)
cosAcosB+sinAsinB=cos(A-B)
cosAcosB-sinAsinB=cos(A+B)
tan(A+B)=(tanA+tanB)/(1-tanAtanB)

=sin(45+30)/cos(45+30)
=tan(45+30)
=(tan45+tan30)/(1-tan45tan30)
=(1+根号3/3)/(1-根号3/3)
=(3+根号3)/(3-根号3)
=(12+6根号3)/6
=2+根号3

Answer 2

在单元格中输入=(SIN(3.14/4)*COS(3.14/6)+COS(3.14/4)*SIN(3.14/6))/(COS(3.14/4)*COS(3.14/6)-SIN(3.14/4)*SIN(3.14/6))，结果为3.72216884

Answer 3

sin45cos30＋cos45sin30／cos45cos30－sin45sin30
=(√2/2*√3/2＋√2/2*1/2)／(√2/2*√3/2－√2/2*1/2)
=(√6+√2)/(√6-√2)=2+√3