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13 February, 00:34

Which of the following is a solution to tan^2 x-1=0? a. 45 degrees, b. 120 degrees, c. 240 degrees, d. 330 degrees

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  1. 13 February, 01:03
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    Do you want a general solution or from 0 < = x < 2pi?

    tan^2 (2x) - 1 = 0

    tan^2 (2x) = 1

    Take the square root of both sides,

    tan (2x) = + / - 1

    Two equations:

    tan (2x) = 1

    tan (2x) = - 1

    Solve each equation.

    tan (2x) = 1, 2x = {pi/4, 5pi/4, 9pi/4, 13pi/4},

    x = { pi/8, 5pi/8, 9pi/8, 13pi/8 }

    tan (2x) = - 1, 2x = { 3pi/4, 7pi/4, 11pi/4, 15pi/4 },

    x = { 3pi/8, 7pi/8, 11pi/8, 15pi/8}

    So for solutions within [0, 2pi),

    x = {pi/8, 3pi/8, 5pi/8, 7pi/8, 9pi/8, 11pi/8, 13pi/8, 15pi/8 }
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