Question

If a+b =π/4
then prove that, (1 + tana) (1 + tanb) = 2
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Answer 1

Answer:

Step-by-step explanation:

a+b =π/4

Tan(a+b) = Tanπ/4

Tana + Tanb /  1 - TanaTanb = 1

Tana + Tanb = 1 - TanaTanb

Tana + Tanb+TanaTanb = 1

Tana(1 + Tanb) + Tanb = 1

Add 1 on both sides.

Tana(1 + Tanb) + Tanb + 1 = 2

(1 + Tanb)(1 + Tana) = 2.

Hence proved.