Trigonometric Identities Question 17
Question: What is $ \frac{\cot 224{}^\circ -\cot 134{}^\circ }{\cot 226{}^\circ +\cot 316{}^\circ } $ equal to?
Options:
A) $ -\text{cosec }88{}^\circ $
B) $ -\text{cosec 2}{}^\circ $
C) $ -\text{cosec 44}{}^\circ $
D) $ -\text{cosec 46}{}^\circ $
Show Answer
Answer:
Correct Answer: B
Solution:
$ \frac{\cot 224{}^\circ -\cot 134{}^\circ }{\cot 226{}^\circ +cot316{}^\circ } $ $ =\frac{\cot (180{}^\circ +44{}^\circ )-\cot (180{}^\circ -46{}^\circ )}{\cot (180{}^\circ +46{}^\circ )+cot(270{}^\circ +46){}^\circ } $ $ =\frac{\cot 44{}^\circ +\cot 46{}^\circ }{\cot 46{}^\circ -tan46{}^\circ }=\frac{tan46{}^\circ +tan44{}^\circ }{tan44{}^\circ -tan46{}^\circ } $ $ =\frac{\sin (46{}^\circ +44{}^\circ )}{\sin (44{}^\circ -46{}^\circ )}=-\cos ec2{}^\circ $
BETA
