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Thread: identity

  1. January 21st 2009, 06:57 PM #1
    william
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    identity

    (tan2 θ) / (tan2 θ + 1) is equivalent to...

    a/ cos^2 theta
    b/ tan^2 theta
    c/ sin^2 theta
    d/ 1
    e/ none of the above
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  2. January 21st 2009, 09:40 PM #2
    Isomorphism
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    Quote Originally Posted by william View Post
    (tan2 θ) / (tan2 θ + 1) is equivalent to...

    a/ cos^2 theta
    b/ tan^2 theta
    c/ sin^2 theta
    d/ 1
    e/ none of the above
    I hope you mean \frac{\tan ^2 \theta}{1 + \tan ^2 \theta}?

    \frac{\tan ^2 \theta}{1 + \tan ^2 \theta} = \dfrac{ \frac{\sin ^2 \theta}{\cos ^2 \theta}}{1 + {\frac{\sin ^2 \theta}{\cos ^2 \theta}}} = \frac{\sin ^2 \theta}{\sin ^ 2 \theta + \cos ^2 \theta} = \sin ^2 \theta
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