if A+B=45 degree.show that {1+tanA}{1+tanB}=2

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 Given A+B=45
  {Take tan on both the sides }

tan(A+B) = tan45 

tanA+tanB/1- tanA tanB = 1

tanA+tanB=1-tanA.tanB

tanA+tanB+tanA.tanB=1

adding "1" on both sides

1+ tanA+tanB+tanA.tanB=1+1

(1 + tanA)+tanB(1+tanA).=2

(1+tanA)(1+tanB)=2  

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Answer below 😊

?A+B=45

tan(A+B)= tan45

tanA+tanB/1- tanAtanB=1

tanA+ tanB= 1-tanAtanB

tanA +tanB+ tanAtanB=1

1+tanA?+tanB+ tanAtanB=1+1 ? ? (adding 1 on both sides)

1(1+tanA) +tanB(1+tanA) =2

(1+tanA)(1+tanB)=2

HENCE, PROVED.