Questions: tan θ cot θ=1

Transcript text: $\tan \theta \cot \theta=1$

Solution

Step 1: Recall the definitions of $\tan \theta$ and $\cot \theta$

\[ \tan \theta = \frac{\sin \theta}{\cos \theta} \quad \text{and} \quad \cot \theta = \frac{\cos \theta}{\sin \theta} \]

Step 2: Multiply $\tan \theta$ and $\cot \theta$

\[ \tan \theta \cdot \cot \theta = \left(\frac{\sin \theta}{\cos \theta}\right) \cdot \left(\frac{\cos \theta}{\sin \theta}\right) \]

Step 3: Simplify the expression

\[ \tan \theta \cdot \cot \theta = \frac{\sin \theta \cdot \cos \theta}{\cos \theta \cdot \sin \theta} = 1 \]

$\boxed{1}$

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