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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.\newlinesin2θcscθ \sin ^{2} \theta \cdot \csc \theta \newlineAnswer:

Full solution

Q. Simplify to a single trig function with no denominator.\newlinesin2θcscθ \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 sin2θ(1sin(θ))\sin^{2}\theta \cdot \left(\frac{1}{\sin(\theta)}\right).
  3. Simplify expression: Simplify sin2θ×(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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