Question

若sinacosb= -1,则sin(a+b)=

Answer 1

sinacosb= -1

故|sina|*|cosb|= |-1|=1

由于0≤|sina|,|cosb|≤1

故|sina|=|cosb|=1

故(cosa)^2=1-(sina)^2=1-1^2=0

(sinb)^2=1-(cosb)^2=1-1^2=0

故cosa=sinb=0

故sin(a+b)=sinacosb+sinbcosa=-1+0*0=-1