A) \[\cot \theta (1-ta{{n}^{2}}\theta )\]
B) \[\cot \theta (ta{{n}^{2}}\theta -1)\]
C) \[\cot \theta ta{{n}^{2}}\theta \]
D) \[tan\theta {{\operatorname{cosec}}^{2}}\theta \]
Correct Answer: B
Solution :
\[\tan \theta \,(1-{{\cot }^{2}}\theta )=\tan \theta \left( 1-\frac{1}{{{\tan }^{2}}\theta } \right)\] \[=\tan \theta \frac{({{\tan }^{2}}\theta -1)}{{{\tan }^{2}}\theta }\] \[=\frac{({{\tan }^{2}}\theta -1)}{\tan \theta }\] \[=\cot \theta \,({{\tan }^{2}}\theta -1)\]
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