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Find the value of cottheta*sintheta*sect...

Find the value of `cottheta*sintheta*sectheta`.

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To find the value of \( \cot \theta \cdot \sin \theta \cdot \sec \theta \), we can follow these steps: ### Step 1: Write the expression We start with the expression: \[ \cot \theta \cdot \sin \theta \cdot \sec \theta \] ### Step 2: Substitute the trigonometric identities We know the following identities: - \( \cot \theta = \frac{\cos \theta}{\sin \theta} \) - \( \sec \theta = \frac{1}{\cos \theta} \) Substituting these identities into the expression gives us: \[ \frac{\cos \theta}{\sin \theta} \cdot \sin \theta \cdot \frac{1}{\cos \theta} \] ### Step 3: Simplify the expression Now, we can simplify the expression: \[ \frac{\cos \theta \cdot \sin \theta}{\sin \theta \cdot \cos \theta} \] ### Step 4: Cancel out the common terms The \( \sin \theta \) in the numerator and denominator cancels out, as does the \( \cos \theta \): \[ = 1 \] ### Final Answer Thus, the value of \( \cot \theta \cdot \sin \theta \cdot \sec \theta \) is: \[ \boxed{1} \]
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