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27 November, 07:39

Rewrite the expression in terms of sine and cosine, and simplify as much as possible. (sec w (1 + csc^2 w)) / (csc^2 w)

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  1. 27 November, 08:21
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    (sin^2 w + 1) / cos w.

    Step-by-step explanation:

    Note: sec w = 1 / cos w and csc w = 1 / sin w.

    So we have:

    (sec w (1 + csc^2 w)) / (csc^2 w)

    = 1/cos w (1 + 1 / sin^2 w) / (1 / sin^2 w)

    = (1 / cos w + 1 / sin^2 w cos w) * sin^2 w

    = sin^2 w / cos w + sin^2 w / (sin^2 w cos w)

    = sin^2 w / cos w + 1 / cos w

    = (sin^2 w + 1) / cos w.
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