已知-π/2<x<0,sinx+cosx=1/5 求3sinx^2-2sinxcosx+cosx^2

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已知-π/2<x<0,sinx+cosx=1/5 求3sinx^2-2sinxcosx+cosx^2

-π/2<x<0,
(sinx+cosx)^2=1+2sinxcosx=1/25
2sinxcosx=-24/25
(sinx-cosx)^2=1-2sinxcosx=49/25
sinx-cosx=±7/5 ∵sinx+cosx=1/5 ,-π/2<x<0,cosx>0
cosx=4/5
3sinx^2-2sinxcosx+cosx^2
=3-2cosx^2 -2sinxcosx
=3-32/25+24/25
=67/25