Pre-cal

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find all solutions of equation in [0, 2pi)
2 (sec x)^2 + (tan x)^2 -3 = 0

  • Pre-cal -

    since sec^2 x = 1+tan^2 x, we have

    2(1+tan^2 x)+tan^2 x-3=0
    3tan^2 x-1 = 0
    tan^2 x = 1/3
    tan x = ±1/√3

    tan x > 0 in QI, QIII, so
    x = π/6, 7π/6

    tan x < 0 in QII, QIV, so
    x = 5π/6, 11π/6

    Actually, since the period of tan x is
    π, it would be better to ask for solutions in [0,π) rather than 2π.

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