以a,b代替α,β
sina+cosb=根号3/2
平方得:
sin^2a+2sinacosb+cos^2b=3/4.(1)
cosa+sinb=根号2
平方得:
cos^2a+2sinbcosa+sin^2b=2.(2)
(1)+(2):
1+2(sinacosb+sinbcosa)+1=11/4
即2sin(a+b)=3/4
sin(a+b)=3/8
tana*cotb
=sina/cosa*cosb/sinb
=(sinacosb)/(cosasinb)