A) \[\frac{1}{a}+\frac{1}{b}\]
B) \[\frac{1}{a}+\frac{1}{b}\]
C) \[a-b\]
D) \[a+b\]
Correct Answer: B
Solution :
| \[\cot \,\,(\theta +\phi )=\frac{1}{\tan \,\,(\theta +\phi )}=\frac{1-\tan q\tan \phi }{\tan \theta +\tan \phi }\] |
| \[=\frac{1}{\tan \theta \tan \phi }-\frac{\tan \theta \tan \phi }{\tan \theta +\tan \phi }\] |
| \[=\frac{1}{\tan \theta +\tan \phi }-\frac{1}{\left( \frac{1}{\tan \theta }+\frac{1}{\tan \phi } \right)}\] |
| \[=\frac{1}{\tan \theta +\tan \theta }-\frac{1}{(\cot \theta +\cot \phi )}\]\[(\because \tan \theta +\tan \phi =a\,\,\text{or}\,\,\cot \theta +\cot \phi =b)\] |
| \[=\frac{1}{a}-\frac{1}{b}\] |
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