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Math Help - 5 Trig questions! (re-post)

  1. #1
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    5 Trig questions! (re-post)

    I need help with these following trig problems..


















    thanks in advanced!
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  2. #2
    Lord of certain Rings
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    ANSWER:

    2 - \tan \theta = 2 - \frac{\sin\theta}{\cos\theta} = \frac{2\cos\theta - \sin \theta}{\cos\theta}

    2\csc \theta - \sec \theta = 2\frac1{\sin\theta} - \frac1{\cos\theta} = \frac{2\cos \theta - \sin \theta}{\sin\theta\cos\theta}

    Now substitute the above expressions:
    \frac{2 - \tan \theta}{2\csc \theta - \sec \theta} = \frac{\frac{2\cos\theta - \sin \theta}{\cos\theta}}{\frac{2\cos \theta - \sin \theta}{\sin\theta\cos\theta}} = \sin \theta






    Do as the hint says:

    2u^2 +5u + 2 = 0
    \Rightarrow u = \frac{-5\pm\sqrt{5^2 - 4(2)(2)}}{2(2)} = \frac{-5\pm3}{4} = -\frac12,-2

    But \cos x \geq -1, -2 root can be discarded.

    Thus you have to solve \cos x = -\frac12.

    I am sure you can handle it from here.
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