Question

若a+b=3派/4 求(1-tan a)(1-tan b)的值

Answer 1

tan(a+b)=(tan a+tan b)/1-tan a*tan b=-1

tan a+tan b=tan a*tan b-1

(1-tan a)(1-tan b)=1-(tan a+tan b)+tan a*tan b

=1-tan a*tan b+1+tan a*tan b=2