A) \[\Pi \,\,\tan \,\,A\]
B) \[\Pi \,\,\cot \,\,A\]
C) \[\Sigma \,{{\tan }^{2}}A\]
D) \[\Sigma \,{{\cot }^{2}}A\]
Correct Answer: A
Solution :
\[\because \] \[A+B+C+D=2\pi \] or \[\tan \,(A+B+C+D)=0\] or \[\frac{\Sigma \,\tan \,A-\Sigma \tan \,A\,\tan \,B\,\tan \,C}{1-\Sigma \tan \,A\,\tan \,B+\tan \,A\,\tan \,B\,\tan \,C\,D}=0\] \[\Rightarrow \] \[\Sigma \tan \,A-\Sigma \tan \,A\,\tan \,B\,\tan \,C=0\] \[\Rightarrow \] \[\Sigma \tan \,A=\tan \,A\,\tan \,B\,\tan \,C\,\tan D\,\,\Sigma \cot \,A\] \[\Rightarrow \] \[\frac{\Sigma \,\tan \,A}{\Sigma \cot \,A}=\Pi \,\tan \,A\]You need to login to perform this action.
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