How is (\cot x) written in terms of (\sin x) and (\cos x)?
Answer and explanation
Correct answer: \(\frac{\cos x}{\sin x}\)
By the quotient identity, \(\cot x=\frac{\cos x}{\sin x}\), so option B is correct. Option A is the formula for \(\tan x=\frac{\sin x}{\cos x}\), not for \(\cot x\). Note that \(\cot x\) is defined only when \(\sin x\ne0\). Exam tip: in \(\tan x\), sine is in the numerator and cosine in the denominator; for \(\cot x\), the order is reversed.
Frequently asked questions
What is the correct answer to this question?
\(\frac{\cos x}{\sin x}\)
Why is this the correct answer?
By the quotient identity, \(\cot x=\frac{\cos x}{\sin x}\), so option B is correct. Option A is the formula for \(\tan x=\frac{\sin x}{\cos x}\), not for \(\cot x\). Note that \(\cot x\) is defined only when \(\sin x\ne0\). Exam tip: in \(\tan x\), sine is in the numerator and cosine in the denominator; for \(\cot x\), the order is reversed.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Trigonometric Functions. Topic: Trigonometric functions and their properties.
