A) 2
B) 0
C) 1
D) \[\frac{1}{2}\]
Correct Answer: C
Solution :
Expression \[=(cosecA-sinA)(secA-cosA)(tanA+cotA)\] \[=\left( \frac{1}{sinA}-\operatorname{sinA} \right)\left( \frac{1}{\cos A}-\cos A \right)\] \[\left( \frac{\operatorname{sinA}}{\cos A}+\frac{\cos A}{\operatorname{sinA}} \right)\]] \[=\left( \frac{1-{{\sin }^{2}}A}{\sin A} \right)\left( \frac{1-{{\cos }^{2}}A}{\cos A} \right)\] \[\left( \frac{{{\sin }^{2}}A+{{\cos }^{2}}A}{\operatorname{sinA}.cosA} \right)\] \[=\frac{{{\cos }^{2}}A.{{\sin }^{2}}A}{{{\sin }^{2}}A.{{\cos }^{2}}A}=1\]
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