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Simplify to a single trig function with no denominator. cot theta*tan theta Answer: theta

Simplify to a single trig function with no denominator.\newlinecot⁡θ⋅tan⁡θ \cot \theta \cdot \tan \theta \newlineAnswer:

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Q. Simplify to a single trig function with no denominator.\newlinecot⁡θ⋅tan⁡θ \cot \theta \cdot \tan \theta \newlineAnswer:
  1. Trigonometric Identity for Cotangent: The trigonometric identity for cotangent is cot⁡(θ)=1tan⁡(θ)\cot(\theta) = \frac{1}{\tan(\theta)}. Therefore, when we multiply cot⁡(θ)\cot(\theta) by tan⁡(θ)\tan(\theta), we get cot⁡(θ)tan⁡(θ)=(1tan⁡(θ))tan⁡(θ)\cot(\theta)\tan(\theta) = \left(\frac{1}{\tan(\theta)}\right)\tan(\theta).
  2. Multiplying Cotangent by Tangent: When we multiply (1/tan⁡(θ))(1/\tan(\theta)) by tan⁡(θ)\tan(\theta), the tan⁡(θ)\tan(\theta) in the numerator and the denominator cancel each other out, leaving us with 11.
  3. Simplifying to 11: Since there are no more operations to perform, we have simplified cot⁡(θ)tan⁡(θ)\cot(\theta)\tan(\theta) to its simplest form, which is 11.

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