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what's the value of A if cot^A(1 - 3 sec A + 2 sec^2 A)=1 and A>90 degrees.

  • maths -

    I assume you mean

    cot^2 A(1 - 3 sec A + 2 sec^2 A)=1

    If so, then

    1 - 3 sec A + 2 sec^2 A = tan^2 A
    sec^2 A - 3sec A + 2
    (secA-1)(secA-2) = 0
    secA=1 so A=0
    secA=2 so A=π/3 or 5π/3

    Looks like 5π/3 is the only solution > π/2

    Check:

    cot^2 5π/3 = 1/3
    1 - 3 sec 5π/3 + 2 sec^2 5π/3 = 1-6+8 = 3

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