tan(a+b)=2/5,tan(b-π/4)=1/4,则tan(a+π/4)的值是多少?

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tan(a+b)=2/5,tan(b-π/4)=1/4,则tan(a+π/4)的值是多少?tan(a+b)=2/5,tan(b-π/4)=1/4,则tan(a+π/4)的值是多少?tan(a+b)=2

tan(a+b)=2/5,tan(b-π/4)=1/4,则tan(a+π/4)的值是多少?
tan(a+b)=2/5,tan(b-π/4)=1/4,则tan(a+π/4)的值是多少?

tan(a+b)=2/5,tan(b-π/4)=1/4,则tan(a+π/4)的值是多少?
答:
tan(a+π/4)
=tan[(a+b)-(b-π/4)]
=[tan(a+b)-tan(b-π/4)]/[1+tan(a+b)tan(b-π/4]
=(2/5-1/4)/(1+2/5×1/4)
=3/22.