A) \[x-y\]
B) \[x+y\]
C) \[\frac{1}{x}-\frac{1}{y}\]
D) \[\frac{1}{x}+\frac{1}{y}\]
Correct Answer: D
Solution :
\[\cot \,B-\cot \,A=y\] or \[\frac{\tan \,A-\tan B}{\tan A\,\tan B}=y\] or \[\tan A\,\tan \,B=\frac{x}{y}\] Now, \[\cot \,(A-B)=\frac{1}{\tan \,(A-B)}\] \[=\frac{1+\tan A\,\tan B}{\tan A-\tan B}\] \[=\frac{1+\frac{x}{y}}{x}=\frac{1}{x}+\frac{1}{y}\]You need to login to perform this action.
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