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trigonometry

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I need help in understanding how to identify which identity to use. using this question as an example.
Show that tan theta (sin theta+cot theta cos theata)all over cos theta = sec^2 theta. Please explain.

  • trigonometry -

    tan(sin+cot*cos)/cos

    When dealing with such a combination of functions, it is usually good to start out by converting everything to sin and cos:

    (sin/cos)(sin+(cos/sin)cos)/cos
    sin/cos * (sin^2 + cos^2)/sin * 1/cos
    (sin^2 + cos^2)/cos^2
    1/cos^2
    sec^2

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