Trig

Find all solutions of the equation on the interval [0,2pi):

Tan^2x=1-secx

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  1. In google type:
    wolfram alpha

    When you see lis of results click on:
    Wolfram Alpha:Computational Knowledge Engine

    When page be open in rectangle type:

    solve tan^2(x)=1-sec(x)

    and click option =

    After few secons you will see result.
    Then clic option Show steps

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  2. Remark:

    When you see step

    Simplify trigonometric functions:

    If we know that:

    tan^2(x)=sec^2(x)-1

    tan^2(x)+sec^2(x)-1=0 becomes:

    sec^2(x)-1+sec(x)-1=0

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  3. sec^2 x - 1= 1 - secx
    sec^2 x + sec x - 2 = 0
    (secx + 2)(secx -1) = 0
    secx = -2 or secx = 1
    cosx = -1/2 or cosx = 1

    x = 120° or x = 240° or x = 0 or x = 360°

    x = 0, 2π/3 , 4π/3, 2π

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  4. Thank you!

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  5. find all solutions to the equation 2x^3+12x^2+50x=0

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