tan(a+b)=2/5,tan(a-90)=1/4,tan(b+90)=?

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tan(a+b)=2/5,tan(a-90)=1/4,tan(b+90)=?tan(a+b)=2/5,tan(a-90)=1/4,tan(b+90)=?tan(a+b)=2/5,tan(a-90)=1

tan(a+b)=2/5,tan(a-90)=1/4,tan(b+90)=?
tan(a+b)=2/5,tan(a-90)=1/4,tan(b+90)=?

tan(a+b)=2/5,tan(a-90)=1/4,tan(b+90)=?
∵tan(a+b)=2/5,tan(a-90)=1/4,
∴tan(b+90)=tan((a+b)-(a-90))
=(tan(a+b)-tan(a-90))/(1+tan(a+b)*tan(a-90))
=((2/5)-(1/4))/(1+(2/5)*(1/4))
=3/22.

设 x=a+b , y=a-90
则 b+90=x-y
所以tan(b+90)
=tan(x-y)
=(tanx-tany)/(1+tanx*tany)