If 0° < θ < 90° and cosecθ = cot²θ,

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If 0° < θ < 90° and cosecθ = cot²θ, then the value of the expression cosec⁴θ – 2cosec⁴θ + cot²θ is equal to:

1. 2
2. 0
3. 1
4. 3

Correct Option: B

cosecθ = cot²θ
⇒ cosecθ = cosec²θ – 1
⇒ cosec²θ – cosecθ = 1 .....(i)
Expression
= cosec⁴θ – 2cosec³θ + cot²θ
= cosec⁴θ – cosec³θ – cosec³θ + cosecθ
= cosec²θ (cosec²θ – cosecθ) – cosecθ (cosec²θ–1)
= cosec²θ – cosec²θ = 0