设tan1234°=a,那么sin(-206°）+cos(-206°）=______.

tan1234°=tan154°=-tan26°=a
tan26°=-a
sin26°= -a/根号（a^2+1）
cos26°= 1/根号（a^2+1）
sin(-206°）+cos(-206°）= -sin26°-cos26°=（a-1）/根号（a^2+1）

tan1234=tan(8*180-206)=tan(-206)=a
sin(-206)/cos(-206)=a
sin(-206)=acos(-206)
[sin(-206)]^2+[cos(-206)]^2=1
sin(-206)=acos(-206)
[cos(-206)]^2=1/(a^2+1)
cos(-206)=-cos26<0
cos(-206)=-1/√(a^2+1)
所以sin(-206)+cos(-206)=acos(-206)+cos(-206)=-(a+1)/√(a^2+1)

sin(-206°）+cos(-206°）=√2【sin（-206°+45°）】=-√2sin161°