A) \[(1-\tan A)\,(1+tanA)\]
B) \[(1+\tan A)\,(cot\,A-1)\]
C) \[(1+\tan A)\,(1-cot\,A)\]
D) \[(\tan \,A-1)\,(\cot \,A-1)\]
Correct Answer: B
Solution :
\[(1-\tan A)\,(\cot \,A+1)\] \[=\left( 1-\frac{1}{\cot \,A} \right)\,\left( \frac{1}{\tan \,A}+1 \right)\] \[=\left( \frac{\cos \,A-1}{\cot \,A} \right)\,\left( \frac{1+\tan \,A}{\tan \,A} \right)\] \[=(1+\tan \,A)(\cot \,A-1)\]
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