A) \[\sqrt{3}\]
B) \[\frac{1}{\sqrt{3}}\]
C) \[3\]
D) \[\frac{1}{3}\]
Correct Answer: C
Solution :
| [c] \[\tan \theta -\cot \theta =0\] \[\Rightarrow \]\[\tan \theta =\cot \theta \]\[\Rightarrow \]\[\tan \theta =\tan (90{}^\circ -\theta )\]\[\Rightarrow \]\[\theta =90{}^\circ -\theta \] \[\Rightarrow \] \[2\theta =90{}^\circ \] \[\therefore \] \[\theta =45{}^\circ \] Then, \[\frac{\tan (\theta +15{}^\circ )}{\tan (\theta -15{}^\circ )}=\frac{\tan (45{}^\circ +15{}^\circ )}{\tan (45{}^\circ -15{}^\circ )}=\frac{\tan 60{}^\circ }{\tan 30{}^\circ }=\frac{\sqrt{3}}{\frac{1}{\sqrt{3}}}=3\] |
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