| The value of \[\cot \frac{\pi }{2}\cot \frac{3\pi }{20}\cot \frac{5\pi }{20}\cot \frac{7\pi }{20}\cot \frac{9\pi }{20}\] [SSC (CGL) 2011] |
A) \[-1\]
B) \[\frac{1}{2}\]
C) \[0\]
D) \[1\]
Correct Answer: D
Solution :
| \[\cot \frac{\pi }{20}\cdot \cot \frac{3\pi }{20}\cdot \cot \frac{5\pi }{20}\cdot \cot \frac{7\pi }{20}\cot \frac{9\pi }{20}\cdot \] |
| \[=\cot \left( \frac{\pi }{2}-\frac{9\pi }{20} \right)\cot \left( \frac{\pi }{2}-\frac{7\pi }{20} \right)\cot \left( \frac{\pi }{4} \right)\cot \frac{7\pi }{20}\cot \frac{9\pi }{20}\] |
| \[=\tan \left( \frac{9\pi }{20} \right)\tan \left( \frac{7\pi }{20} \right)\cot \left( \frac{\pi }{4} \right)\cot \left( \frac{7\pi }{20} \right)\cot \left( \frac{9\pi }{20} \right)\] |
| \[=1.1.1=1\] \[\left[ \because \cot \frac{\pi }{4}=1\,\text{and}\,\text{cot}\theta \cdot \text{tan}\theta =\text{1} \right]\] |
You need to login to perform this action.
You will be redirected in
3 sec
