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Math Help - simplifying trig identity

  1. #1
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    simplifying trig identity

    Hi. looking for help with simplifying an identity. The identity to be simplified is:
    tan^4x + 2tan^2x + 1.

    I'm confident that 2tan^2x + 1 will break down into:
    tan^2x + tan^2x + 1 which equals tan^2x + sec^2x. But I'm not sure how to treat the tan^4 when converting to secant.

    Any help will be much appreciate.
    Mike Clemmons
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  2. #2
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    Quote Originally Posted by Mike Clemmons View Post
    Hi. looking for help with simplifying an identity. The identity to be simplified is:
    tan^4x + 2tan^2x + 1.

    I'm confident that 2tan^2x + 1 will break down into:
    tan^2x + tan^2x + 1 which equals tan^2x + sec^2x. But I'm not sure how to treat the tan^4 when converting to secant.

    Any help will be much appreciate.
    Mike Clemmons
    Note that the problem is in the form

    y^4+2y^2+1=(y^2+1)^2

    where y=\tan(x)

    This should get you started.
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  3. #3
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    Also recall that \tan^2{\theta} + 1 = \sec^2{\theta}.
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