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Simplify to a single trig function with no denominator. sin^(2)theta*csc theta Answer: theta

Simplify to a single trig function with no denominator.\newlinesin⁡2θ⋅csc⁡θ \sin ^{2} \theta \cdot \csc \theta \newlineAnswer:

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Q. Simplify to a single trig function with no denominator.\newlinesin⁡2θ⋅csc⁡θ \sin ^{2} \theta \cdot \csc \theta \newlineAnswer:
  1. Express csc⁡(θ)\csc(\theta): Express csc⁡(θ)\csc(\theta) in terms of sin⁡(θ)\sin(\theta) as csc⁡(θ)=1sin⁡(θ)\csc(\theta) = \frac{1}{\sin(\theta)}.
  2. Substitute csc⁡(θ)\csc(\theta): Substitute csc⁡(θ)\csc(\theta) with 1sin⁡(θ)\frac{1}{\sin(\theta)} in the given expression to get sin⁡2θ⋅(1sin⁡(θ))\sin^{2}\theta \cdot \left(\frac{1}{\sin(\theta)}\right).
  3. Simplify expression: Simplify sin⁡2θ×(1sin⁡(θ))\sin^{2}\theta \times \left(\frac{1}{\sin(\theta)}\right) by canceling one sin⁡(θ)\sin(\theta) in the numerator with the sin⁡(θ)\sin(\theta) in the denominator to get sin⁡(θ)\sin(\theta).

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