已知tan (a+π/4)=7,cosb=5/13,a,b均为锐角,(1)求tana,(2)cos(a+b)

tan(a+π/4)=7
(tana+1)/(1-tana)=7
tana+1=7-7tana
8tana=6
tana=3/4
sina/cosa=3/4
sin²a/cos²a=9/16
16sin²a=9cos²a
25sin²a=9(cos²a+sin²a)
sina=±3/5 cosa=±4/5
因为 a是锐角 所以sina=3/5 cosa=4/5
cosb=5/13 因为b是锐角 所以sinb>0
sinb=12/13
cos(a+b)=cosacosb-sinasinb=4/5×5/13-3/5×12/13=20/65-36/65=-16/65

tan (a+π/4)=7
(tana+tanπ/4)/(1-tanatanπ/4)=7
(tana+1)/(1-tana)=7
tana+1=7(1-tana)
tana+1=7-7tana
8tana=6
tana=3/4
a为锐角
sina=3/5
cosa=4/5
cosb=5/13
b为锐角
sinb=12/13
cos(a+b)
=cosacosb-sinasinb
=4/5*5/13-3/5*12/13
=20/65-36/65
=-16/65