铁路警察给房补吗:若tan(A+B)=2/5,tan(B-pai/4)=1/4,那么tan(A+pai/4)的值是多少.

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解:tan[A+(π/4)]=tan{(A+B)-[B-(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)]
=(3/20)/(22/20)
=3/22

解:tan[A+(π/4)]=tan{(A+B)-[B-(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)]
=(3/20)/(22/20)
=3/22