A) 1
B) \[\frac{3}{2}\]
C) 2
D) 0
Correct Answer: A
Solution :
\[\left( sec\theta -cos\theta \right)\left( cosec\theta -sin\theta \right)\left( tan\theta +cot\theta \right)\] \[=\left( \frac{1}{\cos \theta }-\cos \theta \right)\left( \frac{1}{\sin \theta }-\sin \theta \right)\left( \frac{\sin \theta }{\cos \theta }+\frac{\cos \theta }{\sin \theta } \right)\] \[\left( \frac{1-{{\cos }^{2}}\theta }{\cos \theta } \right)\left( \frac{1-{{\sin }^{2}}\theta }{\sin \theta } \right)\left( \frac{{{\sin }^{2}}\theta +{{\cos }^{2}}\theta }{\sin \theta .cos\theta } \right)\] \[=\frac{{{\sin }^{2}}\theta }{\cos \theta }.\frac{{{\cos }^{2}}\theta }{\sin \theta }.\frac{1}{\sin \theta .\cos \theta }=1\]
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