if a-b=pi by 4is equal to pi by 4 then 1 + tan into 1 minus tan b is equal to
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If A-B =pi/4, then what does (1+tan A)(1-tan B) equal?
A-B = 45, or A = 45+B
1+tan A = 1 + tan(45+B)
= 1 +(tan45 + tan B)/[1 - tan 45*tan B}
= 1 +(1+tan B)/(1- tan B)
=[1-tan B+1+tan B]/(1-tanB)
= 2/(1-tan B). Thus
(1+tan A)(1-tan B) = [2/(1-tan B)](1-tan B)
A-B = 45, or A = 45+B
1+tan A = 1 + tan(45+B)
= 1 +(tan45 + tan B)/[1 - tan 45*tan B}
= 1 +(1+tan B)/(1- tan B)
=[1-tan B+1+tan B]/(1-tanB)
= 2/(1-tan B). Thus
(1+tan A)(1-tan B) = [2/(1-tan B)](1-tan B)
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