tan2x-2cosx=0?

NetherCraft 0

Simplify and find the exact solutions of the equation.

1 Answer

  • First add 2 cosx to both sides to get tan 2x = 2 cos x.

    Replace tan 2x with sin 2x / cos 2x then replace sin 2x with 2 sinx cosx and replace cos 2x with 1 – 2 sin^2 x

    Divide both sides by cosx to get rid of it; now you have

    2 sinx / (1 – 2 sin^2 x) = 2

    cross multiply to get 2 – 4 sin^2 x = 2 sinx

    Divide by 2: 1 – 2 sin^2 x = sinx

    Make it equal zero: 2 sin^2 x + sinx – 1 = 0

    FOIL it: (2 sinx – 1)(sin x + 1) = 0

    so sin x = 1/2 or sin x = -1

    Just find the numbers in your domain that work

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