trig

Simplify (tan^2θcsc^2θ-1)/(tan^2θ)
This question totally stumps me. I know that csc^2=1/(sin^2) and tan^2=(sin^2)/(cos^2), but I don't see how I can use these identities to simplify the question. What am I missing?
Help is much appreciated!

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  1. separate it into 2 fractions

    (tan^2θcsc^2θ-1)/(tan^2θ)
    = (tan^2θcsc^2θ)/(tan^2θ) - 1/tan^2θ
    = csc^2θ - cot^2θ
    = 1/sin2θ - cos2θ/sin2θ
    = (1 - cos2θ)/sin2θ
    = sin2θ/sin2θ
    = 1

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    posted by Reiny
  2. the part starting from

    = 1/sin2θ - cos2θ/sin2θ
    = (1 - cos2θ)/sin2θ
    = sin2θ/sin2θ
    = 1

    should say

    = 1/sin^2θ - cos^2θ/sin^2θ
    = (1 - cos^2θ)/sin^2θ
    = sin^2θ/sin^2θ
    = 1

    I was "cut-and-pasting" and left out the ^

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    posted by Reiny
  3. thank you so much for the explanation!

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    posted by Jennifer

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