Question

prove (1+TanA)(1+tanB)=2,A+B=45°​​

Answer 1

Answer:

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 Hence proved .

Answer 2

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Given,

А + B = 45°

⇒ tаn(А + B) = tаn45°

⇒ (tаnА + tаnB)/(1 - tаnАtаnB) = 1

⇒ tаnА + tаnB = 1 - tаnАtаnB

⇒ tаnА + tаnB + tаnАtаnB = 1

∴ (1 + tаnА)(1 + tаnB)

⇒ 1 + tаnB + tаnА + tаnАtаnB

⇒ 1 + 1

⇒ 2 hence            рrоved