已知tan(π⼀4+a)=2,tanβ=1⼀2 (1)求tana的值

(2)求(sin(a+β)-2sinacosβ)/2sinasinβ+cos(a+β)的值
2024-12-29 18:35:13
推荐回答(1个)
回答1:

(1) tan(派/4+A)=2
(tan派/4+tanA)/(1-tan 派/4*tanA)=2
(1+tanA)/(1-tanA)=2
1+tanA=2(1-tanA)
tanA=1/3
(2) 原式=(sinAcosB+sinBcosA-2sinAcosB)/(2sinAsinB+cosAcosB-sinAsinB)
=(sinBcosA-sinAcosB)/(sinAsinB+cosAcosB)
=sin(B-A)/cos(B-A)
=tan(B-A)
=(tanB-tanA)/(1+tanB*tanA)
=(1/2-1/3)/(1+1/2*1/3)
=1/7