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

Simplify to a single trig function with no denominator.\newlinesin⁡θtan⁡θ \frac{\sin \theta}{\tan \theta} \newlineAnswer:

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Full solution

Q. Simplify to a single trig function with no denominator.\newlinesin⁡θtan⁡θ \frac{\sin \theta}{\tan \theta} \newlineAnswer:
  1. Express tan⁡(θ)\tan(\theta): Express tan⁡(θ)\tan(\theta) in terms of sin⁡(θ)\sin(\theta) and cos⁡(θ)\cos(\theta) as tan⁡(θ)=sin⁡(θ)cos⁡(θ)\tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}.
  2. Substitute tan⁡(θ)\tan(\theta): Substitute tan⁡(θ)\tan(\theta) with sin⁡(θ)cos⁡(θ)\frac{\sin(\theta)}{\cos(\theta)} in the given expression to get sin⁡(θ)sin⁡(θ)/cos⁡(θ)\frac{\sin(\theta)}{\sin(\theta)/\cos(\theta)}.
  3. Simplify expression: Simplify (sin⁡(θ))/(sin⁡(θ)/cos⁡(θ))(\sin(\theta))/(\sin(\theta)/\cos(\theta)) by multiplying the numerator and denominator by cos⁡(θ)\cos(\theta) to get (sin⁡(θ)⋅cos⁡(θ))/sin⁡(θ)(\sin(\theta) \cdot \cos(\theta))/\sin(\theta).
  4. Cancel common terms: Cancel out the common sin⁡(θ)\sin(\theta) terms in the numerator and denominator to get cos⁡(θ)\cos(\theta).

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