What is the value of \(\tan \theta \cdot \cot \theta\)?
Answer and explanation
Correct answer: \(1\)
Using the definitions, \(\tan\theta=\frac{\sin\theta}{\cos\theta}\) and \(\cot\theta=\frac{\cos\theta}{\sin\theta}\). Therefore, \(\tan\theta\cdot\cot\theta=\frac{\sin\theta}{\cos\theta}\cdot\frac{\cos\theta}{\sin\theta}=1\), wherever both functions are defined. It is not \(0\); tangent and cotangent are reciprocal ratios. Exam tip: the product of reciprocal trigonometric ratios is usually \(1\).
Frequently asked questions
What is the correct answer to this question?
\(1\)
Why is this the correct answer?
Using the definitions, \(\tan\theta=\frac{\sin\theta}{\cos\theta}\) and \(\cot\theta=\frac{\cos\theta}{\sin\theta}\). Therefore, \(\tan\theta\cdot\cot\theta=\frac{\sin\theta}{\cos\theta}\cdot\frac{\cos\theta}{\sin\theta}=1\), wherever both functions are defined. It is not \(0\); tangent and cotangent are reciprocal ratios. Exam tip: the product of reciprocal trigonometric ratios is usually \(1\).
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Trigonometric Functions. Topic: Trigonometric functions and their properties.
