【高一数学】同角三角函数的化简求值》》》》

(tanx)/(tanx-1)=-1
tanx=1-tanx
tanx=1/2
sinx/cosx=tanx=1/2
cosx=2sin
所以(sinx-3cosx)/(sinx+cosx)
=(sinx-6sinx)/(sinx+2sinx)
=-5sinx/3sinx
=-5/3
cosx=2sinx
(sinx)^2+(cosx)^2=1
所以(sinx)^2=1/5
(cosx)^2=4/5
sinx/cosx=1/2>0
所以sinxcosx>0
sinxcosx=根号(sinx)^2*(cosx)^2=2/5
所以(sinx)^2+sinxcosx+2=1/5+2/5+2=13/5

(1)(tanx)/(tanx-1)=-1
tanx=1/2
原式上下同时除cosx
=（tanx-3）/（tanx+1）=-5/3
（2）将1化为cos^2x+sin^2x
原式=(sin^2)x+sinxcosx+2sin^2x+2cos^2x
=(3sin^2x+sinxcosx+2cos^2x)/(cos^2x+sin^2x)
上下同时除以cos^2x=(2tan^2x+tanx+2)/1+tan^2x)
=13/5