解方程组：cosa+2sina=-√5.(1)
sin²a+cos²a=1.(2)
把(1)代入(2),
得(2sina+√5)²+sin²a=1
==>5sin²a+4√5sina+4=0
==>(√5sina+2)²=0
==>√5sina+2=0
==>sina=-2/√5
∴ cosa=-1/√5
故 tana=(-2/√5)(-1/√5)=2.
cosa+2sina=-根号5 则tana=?
解方程组：cosa+2sina=-√5.(1)
sin²a+cos²a=1.(2)
把(1)代入(2),
得(2sina+√5)²+sin²a=1
==>5sin²a+4√5sina+4=0
==>(√5sina+2)²=0
==>√5sina+2=0
==>sina=-2/√5
∴ cosa=-1/√5
故 tana=(-2/√5)(-1/√5)=2.