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Math Help - Need steps how to solve this little problem!

  1. #1
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    Exclamation Need steps how to solve this little problem!

    (Trigonometric Functions and Identities)

    1. Which of the following is equivalent to ?

    A. sec2
    B. (csc2) - 1
    C. tan2
    D. sin2
    E.


    Answer = C

    I need to know how they managed to get to C as an answer. Help Please...
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  2. #2
    Super Member Matt Westwood's Avatar
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    One way of going to it is to see that:

    \frac {1 - \cos^2 \theta} {\cos^2 \theta} = \frac {1} {\cos^2 \theta} - \frac {\cos^2 \theta} {\cos^2 \theta} = \sec^2 \theta - 1 = \tan^2 \theta

    ... are you sure you copied the Q down right?
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  3. #3
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    Thank you soo much.

    I am studying for a Compass Math Placement test tomorrow. here is where I got question.
    ACT's COMPASS System: Sample Questions for Trigonometry

    I forgot that the 1 also has the Cos value under it. Thanks for the help.
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  4. #4
    Moo
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    A Cute Angle Moo's Avatar
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    Another one !

    Use identity \sin^2 \theta+\cos^2 \theta=1 \implies 1-\cos^2 \theta=\sin^2 \theta

    So \frac{1-\cos^2 \theta}{\cos^2 \theta}=\frac{\sin^2 \theta}{\cos^2 \theta}=\tan^2 \theta

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