Question

A+B=45, prove the (1+tanA) (1+tanB)=2

Answer 1

Answer:

Step-by-step explanation:

Given, A+B=45=>A=45-B

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

Take lhs

=1+tanB+tanA+tanAtanB

=1+tan(A+B)+tanAtanB

=1+1+0

=2=rhs

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Answer 2

Answer:

The proof is given below

Step-by-step explanation:

Given,

A+B=45

Taking tan on both the sides,

tan(A+B) = tan45

We know forula for tan( A+ B ) and also tan 45 = 1

tanA + tanB / 1 - tanAtanB = 1

tanA+ tanB = 1 - tanAtanB

tanA + tanB + tanAtanB = 1

Adding 1 on both the sides,

1 + tanA + tanB + tanAtanB = 1 + 1    

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

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

Hence,

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