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

Simplify to a single trig function with no denominator.\newlinecsc⁡θsin⁡θ \frac{\csc \theta}{\sin \theta} \newlineAnswer:

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Full solution

Q. Simplify to a single trig function with no denominator.\newlinecsc⁡θsin⁡θ \frac{\csc \theta}{\sin \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 1sin⁡(θ)sin⁡(θ)\frac{\frac{1}{\sin(\theta)}}{\sin(\theta)}.
  3. Simplify expression: Simplify (1sin⁡(θ))/(sin⁡(θ))(\frac{1}{\sin(\theta)})/(\sin(\theta)) as (1sin⁡(θ))⋅(1sin⁡(θ))(\frac{1}{\sin(\theta)})\cdot(\frac{1}{\sin(\theta)}) to get 1sin⁡2(θ)\frac{1}{\sin^2(\theta)}.

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