已知tan(a/2)=2,求tan(a+π/4)的值;(6sina+cosa)/(3sina-2cosa)的值
来源:学生作业帮助网 编辑:作业帮 时间:2024/08/25 20:18:24
![已知tan(a/2)=2,求tan(a+π/4)的值;(6sina+cosa)/(3sina-2cosa)的值](/uploads/image/z/5271410-2-0.jpg?t=%E5%B7%B2%E7%9F%A5tan%EF%BC%88a%2F2%EF%BC%89%3D2%2C%E6%B1%82tan%EF%BC%88a%2B%CF%80%2F4%EF%BC%89%E7%9A%84%E5%80%BC%EF%BC%9B%EF%BC%886sina%2Bcosa%EF%BC%89%2F%EF%BC%883sina-2cosa%EF%BC%89%E7%9A%84%E5%80%BC)
已知tan(a/2)=2,求tan(a+π/4)的值;(6sina+cosa)/(3sina-2cosa)的值
已知tan(a/2)=2,求tan(a+π/4)的值;(6sina+cosa)/(3sina-2cosa)的值
已知tan(a/2)=2,求tan(a+π/4)的值;(6sina+cosa)/(3sina-2cosa)的值
tana=2tan(a/2)/(1-tan^2(a/2))=4/(1-4)=-4/3
所以
tan(a+pi/4)=(1-4/3)/(1+4/3)=-1/7
(6sina+cosa)/(3sina-2cosa)=(6tana+1)/(3tana-2)=(-8+1)/(-4-2)=7/6
1、
tana=2tan(a/2)/[1-tan²(a/2)]=-4/3
所以tan(a+π/4)
=(tana+tanπ/4)/(1-tanatanπ/4)
=(-4/3+1)/{1+4/3)
=-1/7
2
原式分子分母同除以cosa
由sina/cosa=tana
原式=(3tana-2)/(6tana+1)
=(-4-2)/(-8+1)
=6/7
1.
由tana=2tan(a/2)/[1-(tan(a/2)^2)]
得出tana=-4/3
tan(π/4)=1
tan(A+π/4)=(tanA+1)/(1-tanA)=(-4/3+1)/(1+4/3)=-1/7
2.
(6sina+cosa)/(3sina-2cosa)上下都除以cosa
得到(6tana+1)/(3tana-2)=(-8+1)/(-4-2)=7/6
tan a = -4/3 (二倍角)
tan(a+π/4)= -1/7 (拆开)
(6sina+cosa)/(3sina-2cosa)上下同除以cos a
(6tana+1)/(3tana-2)=7/6