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

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

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Full solution

Q. Simplify to a single trig function with no denominator.\newlinecos⁡θsec⁡θ \frac{\cos \theta}{\sec \theta} \newlineAnswer:
  1. Express sec⁡(θ)\sec(\theta): Express sec⁡(θ)\sec(\theta) in terms of cos⁡(θ)\cos(\theta) as sec⁡(θ)=1cos⁡(θ)\sec(\theta) = \frac{1}{\cos(\theta)}.
  2. Substitute sec⁡(θ)\sec(\theta): Substitute sec⁡(θ)\sec(\theta) with 1cos⁡(θ)\frac{1}{\cos(\theta)} in the given expression to get cos⁡(θ)1cos⁡(θ)\frac{\cos(\theta)}{\frac{1}{\cos(\theta)}}.
  3. Simplify expression: Simplify cos⁡(θ)1cos⁡(θ)\frac{\cos(\theta)}{\frac{1}{\cos(\theta)}} as cos⁡(θ)⋅(cos⁡(θ)1)\cos(\theta) \cdot \left(\frac{\cos(\theta)}{1}\right) to get cos⁡2(θ)\cos^2(\theta).

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