sin²x+sinxcosx=6/5,求tanx

sin²x+sinxcosx=6/5,求tanx
sin²x+sinxcosx=6/5,求tanx

sin²x+sinxcosx=6/5,求tanx
sin²x+sinxcosx=6/5
5sin²x+5sinxcosx=6
5sin²x+5sinxcosx=6(sin²x+cos²x)
sin²x-5sinxcosx+6cos²x=0 两边除以cos²x
tan²x-5tanx+6=0
(tanx-2)(tanx-3)=0
tanx=2 tanx=3

(sin²x+sinxcosx)/(sin²x+cos²x)=6/5
上下除cos²x
(tan²x+tanx)/(tan²x+1)=6/5
所以tan²x-5tanx+6=0
所以tanx=2,tanx=3