以a,b代替α,βsina+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)=3/4sin(a+b)=3/8tana*cotb=sina/cosa*cosb/sinb=(sinacosb)/(cosasinb)