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

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

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

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)

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

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)