Question

prove that
(1 + tan A) (1 +tan B)=2tan A if A-B = 45°.​

Answer 1

Step-by-step explanation:

Given that A+B=45°

{Take tan on both 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. Hence proved

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