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What is the sum/difference angle formula for Tan (B-A) ? Quickly please... thank you I can only find Tan (A-B)?

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  • Rogue
    Lv 7
    4 years ago
    Favorite Answer

    they're the same thing if tan(α − β) = (tan(α) − tan(β))/(1 + tan(α)tan(β))

    then tan(B − A) = (tan(B) − tan(A))/(1 + tan(B)tan(A))

    just substitute the variables in the same corresponding place

    tan(30° − 60°) = (tan(30°) − tan(60°))/(1 + tan(30°)tan(60°))

    ∴ tan(30° − 60°) = (√(3)/3 − √(3))/(1 + (√(3)/3)(√3))

    ∴ tan(30° − 60°) = (√(3)/3 − 3√(3)/3)/(1 + 3/3)

    ∴ tan(30° − 60°) = (-2√(3)/3)/2

    ∴ tan(30° − 60°) = -√(3)/3

    tan(60° − 30°) = (tan(60°) − tan(30°))/(1 + tan(60°)tan(30°))

    ∴ tan(60° − 30°) = (√(3) − √(3)/3)/(1 + √(3)(√(3)/3))

    ∴ tan(60° − 30°) = (3√(3)/3 − √(3)/3)/(1 + 3/3)

    ∴ tan(60° − 30°) = (2√(3)/3)/2

    ∴ tan(60° − 30°) = √(3)/3

    Edit however if it will help you understand

    tan(B − A) = tan(-(A − B))

    given tan(-θ) = -tan(θ)

    ∴ tan(B − A) = -tan(A − B)

  • 4 years ago

    Duuuuuhhhhh!

    Use the Tan (A-B) formula, but just switch around the A and the B !!!!!!!!

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