Question

Af A + B = 45° prove that
(1+tan A) (1+tan B) = 2 and
hence deduce the values of tan22*1/2°​

Answer 1

Answer:

Step-by-step explanation:

A+B=45

tan(A+B)=1

tanA+tanB/(1-tanA.tanB)=1

tanA+tanB=1-tanA.tanB

tanA+tanB+tanA.tanB=1

Add 1 both sides

1+tanA+tanB+tanA.tanB=2

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

TanA=(1-cos2A)/sin2A

Put A=22.5°

Tan22.5°=(1-cos45°)/sin45°

Under root(2)-1

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