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

Simplify to a single trig function with no denominator.\newlinecot⁡θcsc⁡θ \frac{\cot \theta}{\csc \theta} \newlineAnswer:

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Full solution

Q. Simplify to a single trig function with no denominator.\newlinecot⁡θcsc⁡θ \frac{\cot \theta}{\csc \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. 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)}.
  3. Substitute csc⁡(θ)\csc(\theta): Substitute csc⁡(θ)\csc(\theta) with 1sin⁡(θ)\frac{1}{\sin(\theta)} in the given expression to get cot⁡(θ)1sin⁡(θ)\frac{\cot(\theta)}{\frac{1}{\sin(\theta)}}.
  4. Simplify expression: Simplify cot⁡(θ)1sin⁡(θ)\frac{\cot(\theta)}{\frac{1}{\sin(\theta)}} as cos⁡(θ)sin⁡(θ)⋅sin⁡(θ)1\frac{\cos(\theta)}{\sin(\theta)} \cdot \frac{\sin(\theta)}{1} to get cos⁡(θ)\cos(\theta).

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