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

Simplify to a single trig function with no denominator.\newlinecos⁡θcot⁡θ \frac{\cos \theta}{\cot \theta} \newlineAnswer:

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Full solution

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

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