A) 1
B) 7
C) 23
D) 25
Correct Answer: C
Solution :
| [c]Given, \[\tan \theta +\cot \theta =5\] |
| Squaring on both sides, we get |
| \[{{(\tan \theta +\cot \theta )}^{2}}={{(5)}^{2}}\] |
| \[\Rightarrow \,\,\,\,\,\,{{\tan }^{2}}\theta +{{\cot }^{2}}\theta +2\tan \theta \cdot \cot \theta =25\] |
| \[\Rightarrow \,\,\,\,\,\,{{\tan }^{2}}\theta +{{\cot }^{2}}\theta +2\tan \theta \cdot \frac{1}{\tan \theta }=25\]\[\left( \cot \theta =\frac{1}{\tan \theta } \right)\] |
| \[\Rightarrow \,\,\,\,\,\,\,\,\,\,{{\tan }^{2}}\theta +{{\cot }^{2}}\theta =25-2\] |
| \[\therefore \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{{\tan }^{2}}\theta +{{\cot }^{2}}\theta =23\] |
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