What is \(\frac{\cosec \theta}{\cot \theta}\) equal to?
Answer and explanation
Correct answer: \(\sec \theta\)
Using \(\cosec\theta=\frac{1}{\sin\theta}\) and \(\cot\theta=\frac{\cos\theta}{\sin\theta}\),
\(\frac{\cosec\theta}{\cot\theta}=\frac{1/\sin\theta}{\cos\theta/\sin\theta}=\frac{1}{\cos\theta}=\sec\theta\). Hence, \(\sec\theta\) is correct. \(\tan\theta\) equals \(\frac{\sin\theta}{\cos\theta}\), so it is not the answer. Exam tip: rewrite reciprocal and quotient trigonometric ratios in terms of \(\sin\theta\) and \(\cos\theta\) before simplifying.
Frequently asked questions
What is the correct answer to this question?
\(\sec \theta\)
Why is this the correct answer?
Using \(\cosec\theta=\frac{1}{\sin\theta}\) and \(\cot\theta=\frac{\cos\theta}{\sin\theta}\),
\(\frac{\cosec\theta}{\cot\theta}=\frac{1/\sin\theta}{\cos\theta/\sin\theta}=\frac{1}{\cos\theta}=\sec\theta\). Hence, \(\sec\theta\) is correct. \(\tan\theta\) equals \(\frac{\sin\theta}{\cos\theta}\), so it is not the answer. Exam tip: rewrite reciprocal and quotient trigonometric ratios in terms of \(\sin\theta\) and \(\cos\theta\) before simplifying.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Trigonometric Functions. Topic: Trigonometric functions and their properties.
