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Couple of basic C3 questions I'm really stuck on. Any help is greatly appreciated. Watch

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    So guys, I've got a few basic C3 questions and I'm really stuck on them, would anyone possibly be able to provide some help?

    Questions are:

    • Find those values of t, to 2 d.p. for which 4sec3 - 7sect + 3 = 0, 0 < t < 2pi
    • Solve the equation (secx-cosx)2 = tanx - sin2x on the interval -2pi < x < 2pi
    • Prove that cos(x+pi/6) + sin(x+pi/3) = (squareroot of 3)cosx


    Any help would be really appreciated. Thanks a lot.
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    (Original post by decb24)
    So guys, I've got a few basic C3 questions and I'm really stuck on them, would anyone possibly be able to provide some help?

    Questions are:
    Find those values of t, to 2 d.p. for which 4sec3 - 7sect + 3 = 0, 0 < t < 2pi
    I assume that this is 4\sec ^3t - 7\sec t + 3 = 0

    It should be clear that one possible solution is that \sec t = 1

    Treat this like any other cubic - divide by (\sec t - 1) and find the solutions for the corresponding quadratic
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    (Original post by decb24)
    So guys, I've got a few basic C3 questions and I'm really stuck on them, would anyone possibly be able to provide some help?

    Questions are:

    • Find those values of t, to 2 d.p. for which 4sec3 - 7sect + 3 = 0, 0 < t < 2pi
    • Solve the equation (secx-cosx)2 = tanx - sin2x on the interval -2pi < x < 2pi
    • Prove that cos(x+pi/6) + sin(x+pi/3) = (squareroot of 3)cosx


    Any help would be really appreciated. Thanks a lot.
    For the third one just use the addition theorems to expand the two terms on the left and use the known values for sin and cos \frac{\pi}{3} \mathrm{ and }\frac{\pi}{6}
 
 
 
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