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