Question

(1+tanA)(1+tan B)=2​

Answer 1

(1+ tan A) (1+tan B ) = 2

Here , a+b = 45° .

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we know that :-

☞ tan ( a+b) = tan A+ tanB / 1 - tan A. tan B

As, a +b = 45°

so tan(45°) = 1

☞ 1 ( 1-tanA. tanB) = tanA +tanB

☞ 1 - tanA.tanB = tanA +tanB

☞ tanA +tanB +tanA.tanB = 1

Adding 1both side :-

☞ 1 +tan A +1 + tanA. tanB = 1+1

☞1( 1+tanA )+ tanB ( 1+tanA) = 2

☞ (1+ tanA) (1+tanB ) = 2

hence proved.