Ved asked in Science & MathematicsMathematics · 3 months ago

. If (1+tanθ)(1+tanϕ) = 2, then what is (θ + ϕ) equal to?

2 Answers

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  • TomV
    Lv 7
    3 months ago

    tan(a+b) = (tan(a) + tan(b)]/[1 - tan(a)tan(b)]

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

    1+tanA +tanB+tanAtanB = 2

    tanA + tanB + tanAtanB = 1

    tanA + tanB = 1 - tanAtanB

    [tanA + tanB]/[1 - tanAtanB] = 1 = tan(A+B)

    tan(A+B) = 1

    A+B = arctan(1) + kπ

    Ans:

     (θ + ϕ) = π/4 + kπ, where k is any integer

    On the interval [0, 2π):

     (θ + ϕ) = π/4, 5π/4

  • 3 months ago

    (1 + tanθ)(1 + tanϕ) = 2

    1 (1 + tanϕ) + tanθ (1 + tanϕ) = 2

    1 + tanϕ + tanθ + tanθ tanϕ = 2

    tanϕ + tanθ = 1 - tanθ tanϕ

    (tanθ + tanϕ) / (1 - tanθ tanϕ) = 1

    tan(θ + ϕ) = 1

    θ + ϕ = 1

    Hence, θ + ϕ = nπ + (π/4), where n is an integer.

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