Tangent Succession
==================

It is know than the tangent of a given angle :math:`\theta` is equivalent to the following mathematical formula involving the sinus and consinus of the same angle:

     :math:`tan \theta = \sqrt{ \frac{1-cos(2\theta)}{1+cos(2\theta)} }`

Implement the following two Python functions in the module :mod:`tangent` (file :file:`tangent.py`).

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The first function is:

    .. py:function:: tanf(a)

such that

    **given** ``a``, a :class:`float` value with the angle in radians, ``a`` diferent than 1.5707963267948966 (equivent to 90 degrees).

    **returns** a :class:`float` with tangent of ``a`` calculated using the above formula, rounded to 4 decimals.

For example:

   .. literalinclude:: tanf-test.txt
      :language: python3
      :start-after: --ini
      :end-before: --fi

.. note:: Python standard modules such as :mod:`math` **may** be imported and used.

Doctests are available at the :download:`tanf-test.txt` file.

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The second function is:

    .. py:function:: tanf5(ad)

such that

    **given** ``ad`` :class:`float` value with the angle in **degrees**

    **returns** the five :class:`float` values obtained by applying the previous function subsequently.
    That means that the function ``tanf`` is applied to given angle ``ad`` (properly converted into radians). Then the result obtained is used as input to ``tanf`` yielding the second value and so on.


For example:

   .. literalinclude:: tanf5-test.txt
      :language: python3
      :start-after: --ini
      :end-before: --fi

.. warning:: This function implementation **must** call the previous function as many times as needed.

Doctests for validation are available at the :download:`tanf5-test.txt` file.