| \[\frac{\tan A+\tan B}{\cot A+\cot \,B}\] is equal to [SSC (CGL) Pre 2011] |
A) \[\cot A\,\cot B\]
B) \[\sec A\,\text{cosec}\,B\]
C) \[\tan A\,\tan B\]
D) None of these
Correct Answer: C
Solution :
| \[\frac{\tan A+\tan B}{\cot A+\cot B}\,\,=\,\,\frac{\tan A+\tan B}{\frac{1}{\tan A}+\frac{1}{\tan B}}\] |
| \[=\,\,\frac{\tan B+\tan B}{\frac{\tan B+\tan A}{\tan A\cdot \tan B}}\,\,=\,\,\frac{1}{\frac{1}{\tan A\cdot \tan B}}\] |
| \[=\tan A\cdot \tan B\] |
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