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Math Help - Fundamental identities to simplify

  1. #1
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    Fundamental identities to simplify

    simplify:
    (tan^2theta)/(sec^2theta)

    still trying to find how to start out haha but cant seem to find out if anyone can help im really struggling with this...
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  2. #2
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    Quote Originally Posted by UserPanther View Post
    simplify:
    (tan^2theta)/(sec^2theta)

    still trying to find how to start out haha but cant seem to find out if anyone can help im really struggling with this...
    Remember that \sec^2{\theta} = \tan^2{\theta} + 1

    So \tan^2{\theta} = \sec^2{\theta} - 1.

    Also recall that \sin^2{\theta} + \cos^2{\theta} = 1.


    Therefore

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

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

     = 1 - \cos^2{\theta}

     = \sin^2{\theta}.
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  3. #3
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    Thank you so much i see how you did it i just need to get used to using all the identities
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