# 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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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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3. thank you so much for the explanation!

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