Solving trig functions! urgent please help!

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1.2sinxtanx + tanx-2sinx-1=0
2.6tan^2x-4sin^2x=1

Both functions is for 0<x<2pi

thank you!

  • Solving trig functions! urgent please help! -

    2 sin^2x/cosx + sinx/cosx - 2 sinx - 1 = 0

    2 sin^2x + sinx -2 sinxcosx - cosx = 0
    2sinx(sinx-cosx) = -(sinx-cosx)
    sinx = -1/2
    x = 210 degrees(7pi/6) or 330degrees(11pi/6)

  • Solving trig functions! urgent please help! -

    6 (sin^2/cos^2) -4 sin^2 - 1 = 0

    6 s^2 - 4 s^2c^2 - c^2 = 0

    6 s^2 -4s^2(1-s^2) -(1-s^2) = 0

    6s^2 -4s^2 +4s^4 +s^2 - 1 = 0

    4 s^4 +3 s^2 -1 = 0

    (4s^2-1)(s^2+1) = 0
    sin^2x = 1/4
    or
    sin^2x = -1 (imaginary root)

    sin x = +1/2
    or sin x = -1/2
    You can take it from there.

  • Solving trig functions! urgent please help! -

    In #1, Damon lost 2 answers by just dropping the (sinx-cosx)

    from
    2sinx(sinx-cosx) = -(sinx-cosx)
    2sinx(sinx-cosx) + (sinx-cosx)= 0
    (sinx-cosx)(2sinx + 1) = 0
    sinx = -1/2
    etc, (see above)

    or

    sinx - cosx = 0
    sinx = cosx
    sinx/cosx =1
    tanx = 1
    x = 45° or 225° (π/4 or 5π/4)

    so x = π/4, 5π/4 , 7π/6, 11π/6

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