Question

一道数学题，急需，在线等

若a+b=3π/4,则(1-tana)(1-tanb)=？

Answer 1

tan(a+b)=(tan a+tan b)/(1-tan a *tan b)=tan3π/4=-1
所以tan a+tan b=tan a *tan b -1
所以(1-tana)(1-tanb)=1-（tan a +tan b）+tan a *tan b
=1-(tan a *tan b-1)+tan a *tan b
=1-tan a*tan a+1+tan a *tan b
=2

Answer 2

-1=tan3π/4,=tan(a+b)
=(tana+tanb)/(1-tana*tanb)
所以tana+tanb=tana*tanb-1
所以(1-tana)(1-tanb)=1-(tana+tanb）+tana*tanb
=1-(tana*tanb-1)+tana*tanb=2

Answer 3

tan (a+b)=-1
(tabna+tanb)/(1-tanatanb)=-1
tabna+tanb=tanatanb-1
-tana-tanb+tanatanb=1
1-tana-tanb+tanatanb=2
(1-tana)(1-tanb)=1

Answer 4

tan(a+b)=(tana+tanb)/(1-tanatanb)=-1
tana+tanb=tanatanb-1
(1-tana)(1-tanb)=1-tana-tanb+tanatanb=2