tan(x+π/4)=3求sinxcosx=?

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tan(x+π/4)=3求sinxcosx=?

tan(x+π/4)=3求sinxcosx=?
tan(x+π/4)=3求sinxcosx=?

tan(x+π/4)=3求sinxcosx=?
tan(x+π/4)=3
=(tanx+tanπ/4)/(1-tanxtanπ/4)
=(1+tanx)/(1-tanx)
=3
1+tanx=3-3tanx
4tanx=2
tanx=1/2=sinx/cosx
cosx=2sinx

sin²x+cos²x=1
即5sin²x=1
sin²x=1/5
所以
sinxcosx=2sin²x=2/5