How can I simplify (1/cos2θ) - (1/cot2θ) using trigonometric identities?

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To simplify (1/cos2θ) - (1/cot2θ), start by expressing cot2θ in terms of sine and cosine, which is cot2θ = cos2θ/sin2θ. This allows the expression to be rewritten as (1/cos2θ) - (sin2θ/cos2θ). Combining the fractions yields (1 - sin2θ) / cos2θ. Recognizing that 1 - sin2θ equals cos2θ, the expression simplifies to cos2θ / cos2θ, resulting in 1. The final simplified expression is 1.
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Homework Statement



Simplify the following:

(1/cos2θ) - (1/cot2θ)

Homework Equations



Various trig identities

The Attempt at a Solution



I tried to make cos2θ into 1-sin2θ and cot2θ into csc2θ-1 but still couldn't find any obvious solution. Help?
 
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What do you get if you express cot as something using sines and cosines?? What if you then add up the fractions?
 
Did you try simply inverting both fractions? Does that show similarity to a trigonometric identity that you know?
 

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