What is the simplified value of \(\frac{\sin(\pi-x)}{\cos(\pi+x)}\)?
Answer and explanation
Correct answer: \(-\tan x\)
Using allied-angle identities, \(\sin(\pi-x)=\sin x\) and \(\cos(\pi+x)=-\cos x\). Therefore, \(\frac{\sin(\pi-x)}{\cos(\pi+x)}=\frac{\sin x}{-\cos x}=-\tan x\). \(\tan x\) is the closest distractor, but it misses the negative sign from the denominator. Exam tip: For angles involving \(\pi\pm x\), check the sign of each trigonometric function separately.
Frequently asked questions
What is the correct answer to this question?
\(-\tan x\)
Why is this the correct answer?
Using allied-angle identities, \(\sin(\pi-x)=\sin x\) and \(\cos(\pi+x)=-\cos x\). Therefore, \(\frac{\sin(\pi-x)}{\cos(\pi+x)}=\frac{\sin x}{-\cos x}=-\tan x\). \(\tan x\) is the closest distractor, but it misses the negative sign from the denominator. Exam tip: For angles involving \(\pi\pm x\), check the sign of each trigonometric function separately.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Trigonometric Functions. Topic: Trigonometric functions and their properties.
