What is the simplified value of \(\frac{\cos(2\pi-x)}{\sin(\pi+x)}\)?
Answer and explanation
Correct answer: \(-\cot x\)
Using the identities \(\cos(2\pi-x)=\cos x\) and \(\sin(\pi+x)=-\sin x\),
\[\frac{\cos(2\pi-x)}{\sin(\pi+x)}=\frac{\cos x}{-\sin x}=-\cot x.\]
Therefore, the correct answer is \(-\cot x\). Choosing \(\cot x\) would ignore the negative sign in the denominator. Exam tip: for an angle of the form \(\pi+x\), sine has a negative sign.
Frequently asked questions
What is the correct answer to this question?
\(-\cot x\)
Why is this the correct answer?
Using the identities \(\cos(2\pi-x)=\cos x\) and \(\sin(\pi+x)=-\sin x\),
\[\frac{\cos(2\pi-x)}{\sin(\pi+x)}=\frac{\cos x}{-\sin x}=-\cot x.\]
Therefore, the correct answer is \(-\cot x\). Choosing \(\cot x\) would ignore the negative sign in the denominator. Exam tip: for an angle of the form \(\pi+x\), sine has a negative sign.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Trigonometric Functions. Topic: Trigonometric functions and their properties.
