| Find \[\frac{\tan 18{}^\circ }{\cot 72{}^\circ }-\frac{\cot 72{}^\circ }{\tan 18{}^\circ }\] |
A) \[2\]
B) \[1\]
C) \[0\]
D) \[\sqrt{2}\]
Correct Answer: C
Solution :
| \[\frac{\tan 18{}^\circ }{\cot 72{}^\circ }-\frac{\cot 72{}^\circ }{\tan 18{}^\circ }=\frac{\tan \,\,(90{}^\circ -72{}^\circ )}{\cot 72{}^\circ }-\frac{\cot \,\,(90{}^\circ -18{}^\circ )}{\tan 18{}^\circ }\] |
| \[=\frac{\cot 72{}^\circ }{\cot 72{}^\circ }-\frac{\tan 18{}^\circ }{\tan 18{}^\circ }\] \[[\because \tan \,\,(90{}^\circ -\theta )=\cot \theta ,cot\,\,(90{}^\circ -\theta )=tan\theta ]\] |
| \[=1-1=0\] |
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