Question

TT
If a + B =π/4 , prove that (1 + tan a) (1 + tan B) = 2.​

Answer 1

Step-by-step explanation:

Given,

A+B = π/4

taking tangent both the sides, we get

tan(A+B) = tan(π/4)

or,( tanA+tanB)/(1-tanA. tanB) = 1 {Since, tan(A+B)=( tanA+tanB)/(1-tanA. tanB) and tan(π/4)=1}

or, tanA+tanB = 1-tanA. tanB

or, tanA+tanB+tanA. tanB = 1

Now, adding 1 both sides,

or, tanA+tanB+tanA.tanB+1 = 2

or, tanA+1 + tanB+tanA.tanB = 2

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

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

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

Hence Proved

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